Master File
Joanna Duran, Nikhil Gupta, Max Moro
2019-03-20 19:51:08
User Inputs
output.var = params$output.var
transform.abs = FALSE
log.pred = params$log.pred
norm.pred = FALSE
eda = params$eda
algo.forward.caret = params$algo.forward.caret
algo.backward.caret = params$algo.backward.caret
algo.stepwise.caret = params$algo.stepwise.caret
algo.LASSO.caret = params$algo.LASSO.caret
algo.LARS.caret = params$algo.LARS.caret
message("Parameters used for training/prediction: ")## Parameters used for training/prediction:str(params)## List of 8
## $ output.var : chr "y3"
## $ log.pred : logi TRUE
## $ eda : logi FALSE
## $ algo.forward.caret : logi TRUE
## $ algo.backward.caret: logi TRUE
## $ algo.stepwise.caret: logi TRUE
## $ algo.LASSO.caret : logi TRUE
## $ algo.LARS.caret : logi TRUE# Setup Labels
output.var.tr = if (log.pred == TRUE) paste0(output.var,'.log') else output.var.tr = output.varLoading Data
feat = read.csv('../../Data/features_highprec.csv')
labels = read.csv('../../Data/labels.csv')
predictors = names(dplyr::select(feat,-JobName))
data.ori = inner_join(feat,labels,by='JobName')
#data.ori = inner_join(feat,select_at(labels,c('JobName',output.var)),by='JobName')Data validation
cc = complete.cases(data.ori)
data.notComplete = data.ori[! cc,]
data = data.ori[cc,] %>% select_at(c(predictors,output.var,'JobName'))
message('Original cases: ',nrow(data.ori))## Original cases: 10000message('Non-Complete cases: ',nrow(data.notComplete))## Non-Complete cases: 3020message('Complete cases: ',nrow(data))## Complete cases: 6980summary(dplyr::select_at(data,c('JobName',output.var)))## JobName y3
## Job_00001: 1 Min. : 95.91
## Job_00002: 1 1st Qu.:118.29
## Job_00003: 1 Median :124.03
## Job_00004: 1 Mean :125.40
## Job_00007: 1 3rd Qu.:131.06
## Job_00008: 1 Max. :193.73
## (Other) :6974Output Variable
The Output Variable y3 shows right skewness, so will proceed with a log transformation
Histogram
df=gather(select_at(data,output.var))
ggplot(df, aes(x=value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() 
#stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value))) QQPlot
ggplot(gather(select_at(data,output.var)), aes(sample=value)) +
stat_qq() +
facet_wrap(~key, scales = 'free',ncol=4)
Trasformation of Output Variable from y3 to y3.log
if(log.pred==TRUE) data[[output.var.tr]] = log(data[[output.var]],10) else
data[[output.var.tr]] = data[[output.var]]
df=gather(select_at(data,c(output.var,output.var.tr)))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=2)
ggplot(gather(select_at(data,c(output.var,output.var.tr))), aes(sample=value)) +
stat_qq() +
facet_wrap(~key, scales = 'free',ncol=4)
Best Normalizator y3
Normalization of y3 using bestNormalize package. (suggested orderNorm) This is cool, but I think is too far for the objective of the project
t=bestNormalize::bestNormalize(data[[output.var]])t## Best Normalizing transformation with 6980 Observations
## Estimated Normality Statistics (Pearson P / df, lower => more normal):
## - No transform: 2.9627
## - Box-Cox: 1.426
## - Log_b(x+a): 1.9884
## - sqrt(x+a): 2.4513
## - exp(x): 749.4167
## - arcsinh(x): 1.9884
## - Yeo-Johnson: 1.1169
## - orderNorm: 1.1737
## Estimation method: Out-of-sample via CV with 10 folds and 5 repeats
##
## Based off these, bestNormalize chose:
## Standardized Yeo-Johnson Transformation with 6980 nonmissing obs.:
## Estimated statistics:
## - lambda = -1.998639
## - mean (before standardization) = 0.5003083
## - sd (before standardization) = 5.108542e-06qqnorm(data[[output.var]])
qqnorm(predict(t))
orderNorm() is a rank-based procedure by which the values of a vector are mapped to their percentile, which is then mapped to the same percentile of the normal distribution. Without the presence of ties, this essentially guarantees that the transformation leads to a uniform distribution
Predictors
All predictors show a Fat-Tail situation, where the two tails are very tall, and a low distribution around the mean. The orderNorm transformation can help (see [Best Normalizator] section)
Interesting Predictors
Histograms
if (eda == TRUE){
cols = c('x11','x18','stat98','x7','stat110')
df=gather(select_at(data,cols))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=3)
# ggplot(gather(select_at(data,cols)), aes(sample=value)) +
# stat_qq()+
# facet_wrap(~key, scales = 'free',ncol=2)
lapply(select_at(data,cols),summary)
}Scatter plot vs. output variable **y3.log
if (eda == TRUE){
d = gather(dplyr::select_at(data,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light green',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=3)
}All Predictors
Histograms
All indicators have a strong indication of Fat-Tails
if (eda == TRUE){
df=gather(select_at(data,predictors))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=4)
}Correlations
With Output Variable
if (eda == TRUE){
#chart.Correlation(select(data,-JobName), pch=21)
t=as.data.frame(round(cor(dplyr::select(data,-one_of(output.var.tr,'JobName'))
,select_at(data,output.var.tr)),4)) %>%
rownames_to_column(var='variable') %>% filter(variable != !!output.var) %>% arrange(-y3.log)
#DT::datatable(t)
message("Top Positive")
kable(head(arrange(t,desc(y3.log)),20))
message("Top Negative")
kable(head(arrange(t,y3.log),20))
}Between All Variables
if (eda == TRUE){
#chart.Correlation(select(data,-JobName), pch=21)
t=as.data.frame(round(cor(dplyr::select(data,-one_of('JobName'))),4))
#DT::datatable(t,options=list(scrollX=T))
message("Showing only 10 variables")
kable(t[1:10,1:10])
}Scatter Plots with Output Variable
Scatter plots with all predictors and the output variable (y3.log)
if (eda == TRUE){
d = gather(dplyr::select_at(data,c(predictors,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)
}Multicollinearity - VIF
No Multicollinearity among predictors
Showing Top predictor by VIF Value
if (eda == TRUE){
vifDF = usdm::vif(select_at(data,predictors)) %>% arrange(desc(VIF))
head(vifDF,15)
}Feature Eng
- Square Root transformation for x18
data.tr=data %>%
mutate(x18.sqrt = sqrt(x18))
cols=c('x18','x18.sqrt')Comparing Pre and Post Transformation Density Plots
# ggplot(gather(select_at(data.tr,cols)), aes(value)) +
# geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
# geom_density() +
# facet_wrap(~key, scales = 'free',ncol=4)
d = gather(dplyr::select_at(data.tr,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
#removing unwanted variables
data.tr=data.tr %>%
dplyr::select_at(names(data.tr)[! names(data.tr) %in% c('x18','y3','JobName')])
data=data.tr
label.names=output.var.trModeling
PCA
# 0 for no interaction,
# 1 for Full 2 way interaction and
# 2 for Selective 2 way interaction
# 3 for Selective 3 way interaction
InteractionMode = 3
pca.vars = names(data)
pca.vars = pca.vars[!pca.vars %in% label.names]
if(InteractionMode == 1){
pca.formula =as.formula(paste0('~(',paste0(pca.vars, collapse ='+'),')^2'))
pca.model = prcomp(formula=pca.formula,data=data[,pca.vars],center=T,scale.=T,retx = T)
#saveRDS(pca.model,'pca.model.rds')
}
if (InteractionMode == 0){
pca.model = prcomp(x=data[,pca.vars],center=T,scale.=T,retx = T)
}
if (InteractionMode >= 2 & InteractionMode <= 3){
controlled.vars = pca.vars[grep("^x",pca.vars)]
stat.vars = pca.vars[grep("^stat",pca.vars)]
if (InteractionMode >= 2){
interaction.form = paste0('~(',paste0(controlled.vars, collapse ='+'),')^2')
}
if (InteractionMode >= 3){
interaction.form = paste0('~(',paste0(controlled.vars, collapse ='+'),')^3')
}
no.interact.form = paste0(stat.vars, collapse ='+')
pca.formula = as.formula(paste(interaction.form, no.interact.form, sep = "+"))
pca.model = prcomp(formula=pca.formula,data=data[,pca.vars],center=T,scale.=T,retx = T)
}targetCumVar = .9
pca.model$var = pca.model$sdev ^ 2 #eigenvalues
pca.model$pvar = pca.model$var / sum(pca.model$var)
pca.model$cumpvar = cumsum(pca.model$pvar )
pca.model$pcaSel = pca.model$cumpvar<=targetCumVar
pca.model$pcaSelCount = sum(pca.model$pcaSel)
pca.model$pcaSelTotVar = sum(pca.model$pvar[pca.model$pcaSel])
message(pca.model$pcaSelCount, " PCAs justify ",percent(targetCumVar)," of the total Variance. (",percent(pca.model$pcaSelTotVar),")")## 156 PCAs justify 90.0% of the total Variance. (90.0%)plot(pca.model$var,xlab="Principal component", ylab="Proportion of variance explained", type='b')
plot(cumsum(pca.model$pvar ),xlab="Principal component", ylab="Cumulative Proportion of variance explained", ylim=c(0,1), type='b')
screeplot(pca.model,npcs = pca.model$pcaSelCount)
screeplot(pca.model,npcs = pca.model$pcaSelCount,type='lines')
#summary(pca.model)
#pca.model$rotation
#creating dataset
data.pca = dplyr::select(data,!!label.names) %>%
dplyr::bind_cols(dplyr::select(as.data.frame(pca.model$x)
,!!colnames(pca.model$rotation)[pca.model$pcaSel])
)Train Test Split
data.pca = data.pca[sample(nrow(data.pca)),] # randomly shuffle data
split = sample.split(data.pca[,label.names], SplitRatio = 0.8)
data.train = subset(data.pca, split == TRUE)
data.test = subset(data.pca, split == FALSE)Common Functions
plot.diagnostics <- function(model, train) {
plot(model)
residuals = resid(model) # Plotted above in plot(lm.out)
r.standard = rstandard(model)
r.student = rstudent(model)
df = data.frame(x=predict(model,train),y=r.student)
p=ggplot(data=df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_hline(yintercept = 0,size=1)+
ylab("Student Residuals") +
xlab("Predicted Values")+
ggtitle("Student Residual Plot")
plot(p)
df = data.frame(x=predict(model,train),y=r.standard)
p=ggplot(data=df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_hline(yintercept = c(-2,0,2),size=1)+
ylab("Student Residuals") +
xlab("Predicted Values")+
ggtitle("Student Residual Plot")
plot(p)
# Histogram
df=data.frame(r.student)
p=ggplot(data=df,aes(r.student)) +
geom_histogram(aes(y=..density..),bins = 50,fill='blue',alpha=0.6) +
stat_function(fun = dnorm, n = 100, args = list(mean = 0, sd = 1)) +
ylab("Density")+
xlab("Studentized Residuals")+
ggtitle("Distribution of Studentized Residuals")
plot(p)
# http://www.stat.columbia.edu/~martin/W2024/R7.pdf
# Influential plots
inf.meas = influence.measures(model)
# print (summary(inf.meas)) # too much data
# Leverage plot
lev = hat(model.matrix(model))
df=tibble::rownames_to_column(as.data.frame(lev),'id')
p=ggplot(data=df,aes(x=as.numeric(id),y=lev)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
ylab('Leverage - check') +
xlab('Index')
plot(p)
# Cook's Distance
cd = cooks.distance(model)
df=tibble::rownames_to_column(as.data.frame(cd),'id')
p=ggplot(data=df,aes(x=as.numeric(id),y=cd)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_text(data=filter(df,cd>15/nrow(train)),aes(label=id),check_overlap=T,size=3,vjust=-.5)+
ylab('Cooks distances') +
geom_hline(yintercept = c(4/nrow(train),0),size=1)+
xlab('Index')
plot(p)
print (paste("Number of data points that have Cook's D > 4/n: ", length(cd[cd > 4/nrow(train)]), sep = ""))
print (paste("Number of data points that have Cook's D > 1: ", length(cd[cd > 1]), sep = ""))
return(cd)
}
# function to set up random seeds
# Based on http://jaehyeon-kim.github.io/2015/05/Setup-Random-Seeds-on-Caret-Package.html
setCaretSeeds <- function(method = "cv", numbers = 1, repeats = 1, tunes = NULL, seed = 1701) {
#B is the number of resamples and integer vector of M (numbers + tune length if any)
B <- if (method == "cv") numbers
else if(method == "repeatedcv") numbers * repeats
else NULL
if(is.null(length)) {
seeds <- NULL
} else {
set.seed(seed = seed)
seeds <- vector(mode = "list", length = B)
seeds <- lapply(seeds, function(x) sample.int(n = 1000000
, size = numbers + ifelse(is.null(tunes), 0, tunes)))
seeds[[length(seeds) + 1]] <- sample.int(n = 1000000, size = 1)
}
# return seeds
seeds
}
train.caret.glmselect = function(formula, data, method
,subopt = NULL, feature.names
, train.control = NULL, tune.grid = NULL, pre.proc = NULL){
if(is.null(train.control)){
train.control <- trainControl(method = "cv"
,number = 10
,seeds = setCaretSeeds(method = "cv"
, numbers = 10
, seed = 1701)
,search = "grid"
,verboseIter = TRUE
,allowParallel = TRUE
)
}
if(is.null(tune.grid)){
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
tune.grid = data.frame(nvmax = 1:length(feature.names))
}
if (method == 'glmnet' && subopt == 'LASSO'){
# Will only show 1 Lambda value during training, but that is OK
# https://stackoverflow.com/questions/47526544/why-need-to-tune-lambda-with-carettrain-method-glmnet-and-cv-glmnet
# Another option for LASSO is this: https://github.com/topepo/caret/blob/master/RegressionTests/Code/lasso.R
lambda = 10^seq(-2,0, length =100)
alpha = c(1)
tune.grid = expand.grid(alpha = alpha,lambda = lambda)
}
if (method == 'lars'){
# https://github.com/topepo/caret/blob/master/RegressionTests/Code/lars.R
fraction = seq(0, 1, length = 100)
tune.grid = expand.grid(fraction = fraction)
pre.proc = c("center", "scale")
}
}
# http://sshaikh.org/2015/05/06/parallelize-machine-learning-in-r-with-multi-core-cpus/
# #cl <- makeCluster(ceiling(detectCores()*0.5)) # use 75% of cores only, leave rest for other tasks
cl <- makeCluster(detectCores()*0.75) # use 75% of cores only, leave rest for other tasks
registerDoParallel(cl)
set.seed(1)
# note that the seed has to actually be set just before this function is called
# settign is above just not ensure reproducibility for some reason
model.caret <- caret::train(formula
, data = data
, method = method
, tuneGrid = tune.grid
, trControl = train.control
, preProc = pre.proc
)
stopCluster(cl)
registerDoSEQ() # register sequential engine in case you are not using this function anymore
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
print("All models results")
print(model.caret$results) # all model results
print("Best Model")
print(model.caret$bestTune) # best model
model = model.caret$finalModel
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-nvmax) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=nvmax,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
# leap function does not support studentized residuals
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
id = rownames(model.caret$bestTune)
# Provides the coefficients of the best model
# regsubsets doens return a full model (see documentation of regsubset), so we need to recalcualte themodel
# https://stackoverflow.com/questions/13063762/how-to-obtain-a-lm-object-from-regsubsets
print("Coefficients of final model:")
coefs <- coef(model, id=id)
#calculate the model to the the coef intervals
nams <- names(coefs)
nams <- nams[!nams %in% "(Intercept)"]
response <- as.character(formula[[2]])
form <- as.formula(paste(response, paste(nams, collapse = " + "), sep = " ~ "))
mod <- lm(form, data = data)
#coefs
#coef(mod)
print(car::Confint(mod))
return(list(model = model,id = id, residPlot = residPlot, residHistogram=residHistogram
,modelLM=mod))
}
if (method == 'glmnet' && subopt == 'LASSO'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
print(model.caret$results)
model=model.caret$finalModel
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-lambda) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=lambda,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
print("Coefficients")
#no interval for glmnet: https://stackoverflow.com/questions/39750965/confidence-intervals-for-ridge-regression
t=coef(model,s=model.caret$bestTune$lambda)
model.coef = t[which(t[,1]!=0),]
print(as.data.frame(model.coef))
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id, residPlot = residPlot, metricsPlot=metricsPlot ))
}
if (method == 'lars'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-fraction) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=fraction,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
print("Coefficients")
t=coef(model.caret$finalModel,s=model.caret$bestTune$fraction,mode='fraction')
model.coef = t[which(t!=0)]
print(model.coef)
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id, residPlot = residPlot, residHistogram=residHistogram))
}
}
# https://stackoverflow.com/questions/48265743/linear-model-subset-selection-goodness-of-fit-with-k-fold-cross-validation
# changed slightly since call[[2]] was just returning "formula" without actually returnign the value in formula
predict.regsubsets <- function(object, newdata, id, formula, ...) {
#form <- as.formula(object$call[[2]])
mat <- model.matrix(formula, newdata) # adds intercept and expands any interaction terms
coefi <- coef(object, id = id)
xvars <- names(coefi)
return(mat[,xvars]%*%coefi)
}
test.model = function(model, test, level=0.95
,draw.limits = FALSE, good = 0.1, ok = 0.15
,method = NULL, subopt = NULL
,id = NULL, formula, feature.names, label.names
,transformation = NULL){
## if using caret for glm select equivalent functionality,
## need to pass formula (full is ok as it will select subset of variables from there)
if (is.null(method)){
pred = predict(model, newdata=test, interval="confidence", level = level)
}
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
pred = predict.regsubsets(model, newdata = test, id = id, formula = formula)
}
if (method == 'glmnet' && subopt == 'LASSO'){
xtest = as.matrix(test[,feature.names])
pred=as.data.frame(predict(model, xtest))
}
if (method == 'lars'){
pred=as.data.frame(predict(model, newdata = test))
}
# Summary of predicted values
print ("Summary of predicted values: ")
print(summary(pred[,1]))
test.mse = mean((test[,label.names]-pred[,1])^2)
print (paste(method, subopt, "Test MSE:", test.mse, sep=" "))
if(log.pred == TRUE || norm.pred == TRUE){
# plot transformewd comparison first
df=data.frame(x=test[,label.names],y=pred[,1])
ggplot(df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_abline(slope=1,intercept=0,color='black',size=1) +
#scale_y_continuous(limits=c(min(df),max(df)))+
xlab("Actual (Transformed)")+
ylab("Predicted (Transformed)")
}
if (log.pred == FALSE && norm.pred == FALSE){
x = test[,label.names]
y = pred[,1]
}
if (log.pred == TRUE){
x = 10^test[,label.names]
y = 10^pred[,1]
}
if (norm.pred == TRUE){
x = predict(transformation, test[,label.names], inverse = TRUE)
y = predict(transformation, pred[,1], inverse = TRUE)
}
df=data.frame(x,y)
ggplot(df,aes(x,y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_abline(slope=c(1+good,1-good,1+ok,1-ok)
,intercept=rep(0,4),color=c('dark green','dark green','dark red','dark red'),size=1,alpha=0.8) +
#scale_y_continuous(limits=c(min(df),max(df)))+
xlab("Actual")+
ylab("Predicted")
}Setup Formulae
n <- names(data.train)
formula <- as.formula(paste(paste(n[n %in% label.names], collapse = " + ")
," ~", paste(n[!n %in% label.names], collapse = " + ")))
grand.mean.formula = as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~ 1"))
print(formula)## y3.log ~ PC1 + PC2 + PC3 + PC4 + PC5 + PC6 + PC7 + PC8 + PC9 +
## PC10 + PC11 + PC12 + PC13 + PC14 + PC15 + PC16 + PC17 + PC18 +
## PC19 + PC20 + PC21 + PC22 + PC23 + PC24 + PC25 + PC26 + PC27 +
## PC28 + PC29 + PC30 + PC31 + PC32 + PC33 + PC34 + PC35 + PC36 +
## PC37 + PC38 + PC39 + PC40 + PC41 + PC42 + PC43 + PC44 + PC45 +
## PC46 + PC47 + PC48 + PC49 + PC50 + PC51 + PC52 + PC53 + PC54 +
## PC55 + PC56 + PC57 + PC58 + PC59 + PC60 + PC61 + PC62 + PC63 +
## PC64 + PC65 + PC66 + PC67 + PC68 + PC69 + PC70 + PC71 + PC72 +
## PC73 + PC74 + PC75 + PC76 + PC77 + PC78 + PC79 + PC80 + PC81 +
## PC82 + PC83 + PC84 + PC85 + PC86 + PC87 + PC88 + PC89 + PC90 +
## PC91 + PC92 + PC93 + PC94 + PC95 + PC96 + PC97 + PC98 + PC99 +
## PC100 + PC101 + PC102 + PC103 + PC104 + PC105 + PC106 + PC107 +
## PC108 + PC109 + PC110 + PC111 + PC112 + PC113 + PC114 + PC115 +
## PC116 + PC117 + PC118 + PC119 + PC120 + PC121 + PC122 + PC123 +
## PC124 + PC125 + PC126 + PC127 + PC128 + PC129 + PC130 + PC131 +
## PC132 + PC133 + PC134 + PC135 + PC136 + PC137 + PC138 + PC139 +
## PC140 + PC141 + PC142 + PC143 + PC144 + PC145 + PC146 + PC147 +
## PC148 + PC149 + PC150 + PC151 + PC152 + PC153 + PC154 + PC155 +
## PC156print(grand.mean.formula)## y3.log ~ 1# Update feature.names because we may have transformed some features
feature.names = n[!n %in% label.names]Full Model
model.full = lm(formula , data.train)
summary(model.full)##
## Call:
## lm(formula = formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.09425 -0.02264 -0.00503 0.01710 0.18637
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.097e+00 4.330e-04 4842.834 < 2e-16 ***
## PC1 2.851e-04 2.901e-05 9.828 < 2e-16 ***
## PC2 -3.788e-04 3.423e-05 -11.065 < 2e-16 ***
## PC3 -8.261e-05 4.099e-05 -2.015 0.043918 *
## PC4 -9.391e-05 4.220e-05 -2.225 0.026117 *
## PC5 -2.385e-04 4.231e-05 -5.637 1.82e-08 ***
## PC6 1.029e-04 4.326e-05 2.378 0.017447 *
## PC7 -1.666e-04 4.386e-05 -3.798 0.000148 ***
## PC8 -1.319e-04 4.502e-05 -2.929 0.003417 **
## PC9 9.820e-05 4.669e-05 2.103 0.035477 *
## PC10 -1.938e-05 4.817e-05 -0.402 0.687420
## PC11 4.749e-04 4.991e-05 9.515 < 2e-16 ***
## PC12 -3.645e-04 5.021e-05 -7.259 4.44e-13 ***
## PC13 3.080e-04 5.180e-05 5.947 2.91e-09 ***
## PC14 5.437e-04 5.248e-05 10.360 < 2e-16 ***
## PC15 -1.099e-04 5.398e-05 -2.037 0.041734 *
## PC16 2.116e-04 5.623e-05 3.764 0.000169 ***
## PC17 -8.012e-05 5.846e-05 -1.371 0.170550
## PC18 -8.213e-05 6.058e-05 -1.356 0.175186
## PC19 -9.287e-05 6.329e-05 -1.468 0.142292
## PC20 3.989e-04 6.777e-05 5.885 4.21e-09 ***
## PC21 -3.618e-04 7.083e-05 -5.109 3.36e-07 ***
## PC22 1.857e-03 7.491e-05 24.791 < 2e-16 ***
## PC23 -5.132e-04 2.145e-04 -2.393 0.016762 *
## PC24 -3.735e-05 2.345e-04 -0.159 0.873470
## PC25 4.272e-04 2.363e-04 1.808 0.070617 .
## PC26 1.483e-04 2.452e-04 0.605 0.545497
## PC27 -1.627e-04 2.517e-04 -0.646 0.518153
## PC28 -1.552e-04 2.531e-04 -0.613 0.539812
## PC29 2.650e-04 2.626e-04 1.009 0.312931
## PC30 -1.212e-04 2.754e-04 -0.440 0.659980
## PC31 -2.074e-04 2.882e-04 -0.719 0.471881
## PC32 1.819e-04 2.981e-04 0.610 0.541825
## PC33 8.708e-06 2.992e-04 0.029 0.976780
## PC34 3.666e-04 3.048e-04 1.203 0.229217
## PC35 4.560e-05 3.062e-04 0.149 0.881617
## PC36 7.130e-05 3.104e-04 0.230 0.818291
## PC37 6.686e-04 3.161e-04 2.115 0.034471 *
## PC38 3.433e-04 3.150e-04 1.090 0.275791
## PC39 -7.474e-04 3.174e-04 -2.354 0.018594 *
## PC40 -3.080e-05 3.203e-04 -0.096 0.923420
## PC41 3.322e-04 3.225e-04 1.030 0.303124
## PC42 2.202e-04 3.223e-04 0.683 0.494639
## PC43 6.501e-05 3.236e-04 0.201 0.840821
## PC44 1.178e-04 3.268e-04 0.360 0.718513
## PC45 3.993e-04 3.275e-04 1.219 0.222865
## PC46 2.721e-04 3.321e-04 0.819 0.412544
## PC47 -6.007e-04 3.303e-04 -1.819 0.069032 .
## PC48 3.744e-04 3.357e-04 1.115 0.264719
## PC49 3.018e-04 3.344e-04 0.902 0.366869
## PC50 6.516e-04 3.369e-04 1.934 0.053117 .
## PC51 -3.713e-04 3.417e-04 -1.087 0.277221
## PC52 -1.187e-03 3.420e-04 -3.471 0.000523 ***
## PC53 -3.275e-04 3.473e-04 -0.943 0.345749
## PC54 1.245e-04 3.444e-04 0.362 0.717703
## PC55 3.457e-04 3.452e-04 1.001 0.316696
## PC56 -3.544e-04 3.524e-04 -1.006 0.314647
## PC57 5.764e-04 3.521e-04 1.637 0.101624
## PC58 1.039e-03 3.525e-04 2.949 0.003205 **
## PC59 3.031e-04 3.537e-04 0.857 0.391421
## PC60 3.875e-05 3.529e-04 0.110 0.912564
## PC61 8.183e-04 3.570e-04 2.292 0.021920 *
## PC62 4.475e-04 3.574e-04 1.252 0.210534
## PC63 6.753e-04 3.586e-04 1.883 0.059730 .
## PC64 2.703e-04 3.582e-04 0.755 0.450398
## PC65 -1.522e-04 3.632e-04 -0.419 0.675100
## PC66 1.565e-04 3.592e-04 0.436 0.663142
## PC67 -6.496e-04 3.653e-04 -1.778 0.075471 .
## PC68 -2.493e-05 3.665e-04 -0.068 0.945777
## PC69 1.045e-03 3.639e-04 2.871 0.004112 **
## PC70 3.648e-04 3.702e-04 0.985 0.324465
## PC71 -5.113e-05 3.693e-04 -0.138 0.889889
## PC72 9.559e-04 3.682e-04 2.596 0.009443 **
## PC73 5.030e-05 3.687e-04 0.136 0.891500
## PC74 3.881e-04 3.714e-04 1.045 0.296052
## PC75 4.399e-04 3.695e-04 1.191 0.233861
## PC76 -3.644e-04 3.721e-04 -0.979 0.327459
## PC77 1.107e-03 3.724e-04 2.974 0.002956 **
## PC78 -2.844e-04 3.719e-04 -0.765 0.444470
## PC79 -1.018e-03 3.725e-04 -2.732 0.006310 **
## PC80 -3.998e-04 3.733e-04 -1.071 0.284132
## PC81 3.806e-04 3.741e-04 1.017 0.309090
## PC82 2.060e-05 3.729e-04 0.055 0.955949
## PC83 -3.473e-04 3.759e-04 -0.924 0.355523
## PC84 2.266e-04 3.767e-04 0.601 0.547566
## PC85 -5.952e-04 3.766e-04 -1.580 0.114097
## PC86 -3.743e-04 3.792e-04 -0.987 0.323762
## PC87 -1.020e-03 3.763e-04 -2.710 0.006743 **
## PC88 2.179e-04 3.802e-04 0.573 0.566548
## PC89 4.171e-04 3.786e-04 1.102 0.270690
## PC90 -7.093e-04 3.788e-04 -1.873 0.061167 .
## PC91 5.165e-04 3.839e-04 1.346 0.178512
## PC92 -7.572e-05 3.813e-04 -0.199 0.842589
## PC93 6.046e-04 3.829e-04 1.579 0.114442
## PC94 1.522e-04 3.822e-04 0.398 0.690553
## PC95 4.533e-04 3.808e-04 1.190 0.233979
## PC96 -3.015e-04 3.813e-04 -0.791 0.429183
## PC97 -1.845e-04 3.840e-04 -0.481 0.630840
## PC98 6.540e-04 3.843e-04 1.702 0.088883 .
## PC99 -1.421e-03 3.856e-04 -3.685 0.000231 ***
## PC100 -4.994e-04 3.868e-04 -1.291 0.196744
## PC101 2.526e-04 3.852e-04 0.656 0.511993
## PC102 3.120e-04 3.874e-04 0.805 0.420739
## PC103 -5.112e-04 3.870e-04 -1.321 0.186582
## PC104 1.592e-04 3.878e-04 0.411 0.681453
## PC105 -4.513e-04 3.915e-04 -1.153 0.249061
## PC106 2.192e-05 3.901e-04 0.056 0.955195
## PC107 -1.273e-03 3.881e-04 -3.279 0.001049 **
## PC108 3.164e-04 3.886e-04 0.814 0.415539
## PC109 4.245e-04 3.943e-04 1.077 0.281696
## PC110 -4.415e-05 3.897e-04 -0.113 0.909790
## PC111 -8.848e-04 3.910e-04 -2.263 0.023695 *
## PC112 -1.163e-03 3.914e-04 -2.972 0.002970 **
## PC113 4.954e-04 3.904e-04 1.269 0.204514
## PC114 7.547e-05 3.900e-04 0.194 0.846551
## PC115 -8.165e-04 3.937e-04 -2.074 0.038115 *
## PC116 1.341e-03 3.896e-04 3.441 0.000585 ***
## PC117 8.247e-04 3.942e-04 2.092 0.036468 *
## PC118 9.646e-04 3.924e-04 2.458 0.013983 *
## PC119 -3.786e-04 3.948e-04 -0.959 0.337689
## PC120 5.851e-04 3.959e-04 1.478 0.139440
## PC121 -2.337e-04 3.958e-04 -0.591 0.554853
## PC122 -1.408e-03 3.927e-04 -3.585 0.000340 ***
## PC123 1.898e-04 3.950e-04 0.481 0.630879
## PC124 1.607e-04 3.972e-04 0.405 0.685818
## PC125 -6.586e-05 3.972e-04 -0.166 0.868323
## PC126 9.596e-04 3.995e-04 2.402 0.016348 *
## PC127 -1.066e-03 3.994e-04 -2.670 0.007604 **
## PC128 -1.616e-05 3.995e-04 -0.040 0.967739
## PC129 -1.770e-04 3.985e-04 -0.444 0.656929
## PC130 5.703e-04 4.009e-04 1.423 0.154934
## PC131 6.614e-05 4.014e-04 0.165 0.869112
## PC132 -1.563e-05 4.036e-04 -0.039 0.969113
## PC133 -1.254e-03 4.005e-04 -3.132 0.001747 **
## PC134 6.838e-04 4.017e-04 1.702 0.088739 .
## PC135 -9.845e-05 4.066e-04 -0.242 0.808714
## PC136 1.243e-04 4.033e-04 0.308 0.757883
## PC137 -8.539e-04 4.064e-04 -2.101 0.035700 *
## PC138 1.573e-04 4.033e-04 0.390 0.696536
## PC139 -7.689e-04 4.075e-04 -1.887 0.059201 .
## PC140 3.405e-04 4.056e-04 0.839 0.401273
## PC141 -1.335e-04 4.053e-04 -0.329 0.741839
## PC142 1.956e-04 4.063e-04 0.481 0.630186
## PC143 1.127e-03 4.059e-04 2.777 0.005498 **
## PC144 6.876e-04 4.090e-04 1.681 0.092825 .
## PC145 -1.132e-04 4.089e-04 -0.277 0.781867
## PC146 2.314e-03 4.096e-04 5.650 1.68e-08 ***
## PC147 -2.315e-04 4.085e-04 -0.567 0.570891
## PC148 -4.911e-04 4.107e-04 -1.196 0.231792
## PC149 -4.523e-05 4.096e-04 -0.110 0.912066
## PC150 -5.764e-04 4.101e-04 -1.405 0.159946
## PC151 -8.713e-05 4.108e-04 -0.212 0.832031
## PC152 -1.260e-03 4.104e-04 -3.071 0.002143 **
## PC153 -6.404e-04 4.106e-04 -1.560 0.118934
## PC154 7.080e-04 4.127e-04 1.716 0.086303 .
## PC155 -5.064e-04 4.130e-04 -1.226 0.220216
## PC156 3.395e-04 4.139e-04 0.820 0.412176
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03225 on 5427 degrees of freedom
## Multiple R-squared: 0.2301, Adjusted R-squared: 0.2079
## F-statistic: 10.4 on 156 and 5427 DF, p-value: < 2.2e-16cd.full = plot.diagnostics(model=model.full, train=data.train)
## [1] "Number of data points that have Cook's D > 4/n: 270"
## [1] "Number of data points that have Cook's D > 1: 0"Checking with removal of high influence points
high.cd = names(cd.full[cd.full > 4/nrow(data.train)])
#save dataset with high.cd flagged
t = data.train %>%
rownames_to_column() %>%
mutate(high.cd = ifelse(rowname %in% high.cd,1,0))
#write.csv(t,file='data_high_cd_flag.csv',row.names = F)
###
data.train2 = data.train[!(rownames(data.train)) %in% high.cd,]
model.full2 = lm(formula , data.train2)
summary(model.full2)##
## Call:
## lm(formula = formula, data = data.train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.076433 -0.020875 -0.002849 0.019196 0.085203
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.094e+00 3.952e-04 5298.868 < 2e-16 ***
## PC1 2.697e-04 2.660e-05 10.136 < 2e-16 ***
## PC2 -3.831e-04 3.141e-05 -12.199 < 2e-16 ***
## PC3 -1.364e-04 3.758e-05 -3.630 0.000286 ***
## PC4 -6.954e-05 3.854e-05 -1.804 0.071215 .
## PC5 -2.346e-04 3.883e-05 -6.040 1.64e-09 ***
## PC6 8.715e-05 3.944e-05 2.210 0.027177 *
## PC7 -1.779e-04 4.021e-05 -4.424 9.90e-06 ***
## PC8 -1.058e-04 4.136e-05 -2.558 0.010567 *
## PC9 1.096e-04 4.285e-05 2.558 0.010558 *
## PC10 2.573e-05 4.402e-05 0.585 0.558867
## PC11 4.992e-04 4.558e-05 10.951 < 2e-16 ***
## PC12 -3.876e-04 4.597e-05 -8.430 < 2e-16 ***
## PC13 2.583e-04 4.748e-05 5.441 5.54e-08 ***
## PC14 6.212e-04 4.819e-05 12.892 < 2e-16 ***
## PC15 -1.272e-04 4.948e-05 -2.571 0.010175 *
## PC16 1.897e-04 5.160e-05 3.676 0.000239 ***
## PC17 -6.545e-05 5.338e-05 -1.226 0.220173
## PC18 -7.167e-05 5.569e-05 -1.287 0.198158
## PC19 -1.125e-04 5.800e-05 -1.939 0.052566 .
## PC20 4.207e-04 6.204e-05 6.781 1.32e-11 ***
## PC21 -2.845e-04 6.453e-05 -4.409 1.06e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02879 on 5292 degrees of freedom
## Multiple R-squared: 0.1335, Adjusted R-squared: 0.1301
## F-statistic: 38.83 on 21 and 5292 DF, p-value: < 2.2e-16cd.full2 = plot.diagnostics(model.full2, data.train2)
## [1] "Number of data points that have Cook's D > 4/n: 202"
## [1] "Number of data points that have Cook's D > 1: 0"# much more normal residuals than before.
# Checking to see if distributions are different and if so whcih variables
# High Leverage Plot
plotData = data.train %>%
rownames_to_column() %>%
mutate(type=ifelse(rowname %in% high.cd,'High','Normal')) %>%
dplyr::select(type,target=one_of(label.names))
ggplot(data=plotData, aes(x=type,y=target)) +
geom_boxplot(fill='light blue',outlier.shape=NA) +
scale_y_continuous(name="Target Variable Values",label=scales::comma_format(accuracy=.1)) +
theme_light() +
ggtitle('Distribution of High Leverage Points and Normal Points')
# 2 sample t-tests
plotData = data.train %>%
rownames_to_column() %>%
mutate(type=ifelse(rowname %in% high.cd,'High','Normal')) %>%
dplyr::select(type,one_of(feature.names))
comp.test = lapply(dplyr::select(plotData, one_of(feature.names))
, function(x) t.test(x ~ plotData$type, var.equal = TRUE))
sig.comp = list.filter(comp.test, p.value < 0.05)
sapply(sig.comp, function(x) x[['p.value']])## PC1 PC14 PC83 PC104 PC112 PC114
## 1.534155e-06 1.032959e-04 5.984026e-03 4.926227e-02 1.902915e-02 2.357616e-02mm = melt(plotData, id=c('type')) %>% filter(variable %in% names(sig.comp))
ggplot(mm,aes(x=type, y=value)) +
geom_boxplot()+
facet_wrap(~variable, ncol=5, scales = 'free_y') +
scale_y_continuous(name="values",label=scales::comma_format(accuracy=.1)) +
ggtitle('Distribution of High Leverage Points and Normal Points')
# Distribution (box) Plots
mm = melt(plotData, id=c('type'))
ggplot(mm,aes(x=type, y=value)) +
geom_boxplot()+
facet_wrap(~variable, ncol=8, scales = 'free_y') +
scale_y_continuous(name="values",label=scales::comma_format(accuracy=.1)) +
ggtitle('Distribution of High Leverage Points and Normal Points')
Grand Means Model
model.null = lm(grand.mean.formula, data.train)
summary(model.null)##
## Call:
## lm(formula = grand.mean.formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.114676 -0.023705 -0.003387 0.020847 0.190636
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.096552 0.000485 4323 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03624 on 5583 degrees of freedomVariable Selection
Basic: http://www.stat.columbia.edu/~martin/W2024/R10.pdf Cross Validation + Other Metrics: http://www.sthda.com/english/articles/37-model-selection-essentials-in-r/154-stepwise-regression-essentials-in-r/
Forward Selection with CV
Train
if (algo.forward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
, data = data.train
, method = "leapForward"
, feature.names = feature.names)
model.forward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 60 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03460715 0.08910629 0.02686885 0.0011220847 0.02445943 0.0006474464
## 2 2 0.03427537 0.10669480 0.02663179 0.0010083889 0.02883392 0.0005758770
## 3 3 0.03411994 0.11496880 0.02653867 0.0010265906 0.03075293 0.0006063719
## 4 4 0.03379615 0.13189897 0.02630712 0.0010207545 0.03344351 0.0005144619
## 5 5 0.03350142 0.14741335 0.02600541 0.0011291975 0.04089043 0.0006240441
## 6 6 0.03335616 0.15492598 0.02585664 0.0011817548 0.04260564 0.0006431018
## 7 7 0.03334671 0.15524765 0.02588207 0.0011918151 0.04207618 0.0006350839
## 8 8 0.03331117 0.15702802 0.02587148 0.0011827844 0.04160488 0.0006327650
## 9 9 0.03322305 0.16163226 0.02580335 0.0012175344 0.04406315 0.0006238541
## 10 10 0.03304920 0.17039248 0.02567687 0.0012542700 0.04567367 0.0006956817
## 11 11 0.03294153 0.17540794 0.02559498 0.0012363522 0.04359549 0.0007022903
## 12 12 0.03302015 0.17164164 0.02563644 0.0012557230 0.04412034 0.0006919223
## 13 13 0.03305043 0.17016840 0.02564263 0.0012468449 0.04189529 0.0007132106
## 14 14 0.03301946 0.17187785 0.02562588 0.0012420740 0.04196257 0.0006972580
## 15 15 0.03304794 0.17044746 0.02565163 0.0012271977 0.04033782 0.0006823314
## 16 16 0.03304618 0.17060985 0.02566269 0.0012216908 0.04034003 0.0006564886
## 17 17 0.03302631 0.17169036 0.02566679 0.0012273896 0.04149103 0.0006758318
## 18 18 0.03299358 0.17333306 0.02564312 0.0012334455 0.04215032 0.0006963940
## 19 19 0.03296701 0.17451230 0.02564028 0.0012021627 0.04090036 0.0006805821
## 20 20 0.03295161 0.17520514 0.02562301 0.0011632949 0.03937627 0.0006490421
## 21 21 0.03294342 0.17569547 0.02561491 0.0011339592 0.03845149 0.0006403542
## 22 22 0.03296495 0.17490667 0.02562498 0.0011555594 0.03944700 0.0006626812
## 23 23 0.03294635 0.17573083 0.02558977 0.0011508121 0.03910113 0.0006454214
## 24 24 0.03293832 0.17614576 0.02559123 0.0011700580 0.03838173 0.0006842952
## 25 25 0.03292094 0.17695723 0.02557273 0.0011747830 0.03836036 0.0006890772
## 26 26 0.03287875 0.17905169 0.02552170 0.0011784192 0.03870279 0.0006941080
## 27 27 0.03288472 0.17889913 0.02553718 0.0011702651 0.03954319 0.0006737343
## 28 28 0.03285560 0.18010664 0.02550215 0.0011583478 0.03826274 0.0006693062
## 29 29 0.03285475 0.18020821 0.02548120 0.0011296991 0.03726967 0.0006298356
## 30 30 0.03281703 0.18202381 0.02546579 0.0011283144 0.03763312 0.0006352938
## 31 31 0.03280656 0.18265860 0.02545133 0.0011510835 0.03825756 0.0006202786
## 32 32 0.03280791 0.18263516 0.02544072 0.0011443911 0.03720283 0.0006090150
## 33 33 0.03279398 0.18328647 0.02543037 0.0011243804 0.03696881 0.0005880315
## 34 34 0.03277028 0.18445467 0.02540484 0.0011235998 0.03730505 0.0006068126
## 35 35 0.03274883 0.18530440 0.02539191 0.0011135069 0.03586909 0.0006076907
## 36 36 0.03274507 0.18551295 0.02539207 0.0010892369 0.03574803 0.0006177277
## 37 37 0.03273283 0.18596732 0.02538464 0.0010481181 0.03410175 0.0005812428
## 38 38 0.03271812 0.18664667 0.02536959 0.0010337151 0.03370093 0.0005685931
## 39 39 0.03274129 0.18560255 0.02539236 0.0010345439 0.03348123 0.0005586956
## 40 40 0.03273552 0.18591130 0.02539526 0.0010355019 0.03309684 0.0005569333
## 41 41 0.03272108 0.18657733 0.02537083 0.0010303174 0.03236046 0.0005471613
## 42 42 0.03271963 0.18666364 0.02537446 0.0010197381 0.03196622 0.0005381671
## 43 43 0.03272124 0.18654185 0.02538236 0.0009911899 0.03159428 0.0005331453
## 44 44 0.03274289 0.18567679 0.02539750 0.0009951781 0.03234625 0.0005310049
## 45 45 0.03275325 0.18539350 0.02541582 0.0010009944 0.03346403 0.0005461326
## 46 46 0.03275542 0.18529239 0.02541128 0.0009914222 0.03250482 0.0005351964
## 47 47 0.03276933 0.18460853 0.02543274 0.0009681256 0.03126429 0.0005136176
## 48 48 0.03274988 0.18562391 0.02541908 0.0009804754 0.03176915 0.0005148088
## 49 49 0.03275553 0.18549823 0.02542525 0.0010007573 0.03211922 0.0005294594
## 50 50 0.03277106 0.18485168 0.02543581 0.0010039392 0.03198443 0.0005320075
## 51 51 0.03277763 0.18450302 0.02543837 0.0009952213 0.03095233 0.0005173043
## 52 52 0.03278798 0.18409848 0.02545199 0.0009908014 0.03089017 0.0005212592
## 53 53 0.03277648 0.18467673 0.02543358 0.0010009955 0.03093738 0.0005100227
## 54 54 0.03276073 0.18545779 0.02541901 0.0009984671 0.03126142 0.0005210751
## 55 55 0.03274715 0.18616129 0.02541850 0.0010127485 0.03203220 0.0005248897
## 56 56 0.03273869 0.18660366 0.02540922 0.0010352073 0.03215573 0.0005547967
## 57 57 0.03270805 0.18803081 0.02539284 0.0010466131 0.03236273 0.0005550320
## 58 58 0.03270979 0.18808059 0.02539751 0.0010551510 0.03266562 0.0005609570
## 59 59 0.03271178 0.18802159 0.02539465 0.0010524592 0.03227840 0.0005608017
## 60 60 0.03269844 0.18866632 0.02538764 0.0010550590 0.03309063 0.0005611154
## 61 61 0.03270491 0.18837209 0.02539294 0.0010625515 0.03314899 0.0005596570
## 62 62 0.03272511 0.18746767 0.02540607 0.0010577008 0.03277498 0.0005637775
## 63 63 0.03272027 0.18765640 0.02540109 0.0010545200 0.03269457 0.0005680688
## 64 64 0.03270861 0.18823243 0.02538868 0.0010488503 0.03268527 0.0005743375
## 65 65 0.03271591 0.18795256 0.02539107 0.0010446916 0.03285781 0.0005841722
## 66 66 0.03271996 0.18775080 0.02539361 0.0010436172 0.03313321 0.0005918850
## 67 67 0.03271843 0.18788949 0.02539473 0.0010417985 0.03311181 0.0005890268
## 68 68 0.03271644 0.18803325 0.02539528 0.0010572510 0.03367356 0.0006088207
## 69 69 0.03272182 0.18777941 0.02540272 0.0010492718 0.03359551 0.0005994725
## 70 70 0.03272822 0.18752142 0.02539644 0.0010454808 0.03360970 0.0006019131
## 71 71 0.03273484 0.18726898 0.02539376 0.0010367535 0.03347874 0.0006027592
## 72 72 0.03273453 0.18725948 0.02538632 0.0010391762 0.03314719 0.0006078312
## 73 73 0.03272984 0.18750358 0.02538296 0.0010293007 0.03315450 0.0006026834
## 74 74 0.03273001 0.18755417 0.02537867 0.0010220918 0.03373738 0.0006058184
## 75 75 0.03272151 0.18796897 0.02536932 0.0010207351 0.03387082 0.0006093350
## 76 76 0.03273155 0.18750763 0.02537749 0.0010264015 0.03372761 0.0006173888
## 77 77 0.03273199 0.18745650 0.02538229 0.0010206493 0.03335904 0.0006102604
## 78 78 0.03274348 0.18701344 0.02539033 0.0010311402 0.03405252 0.0006209184
## 79 79 0.03274018 0.18716972 0.02538595 0.0010328567 0.03409210 0.0006250520
## 80 80 0.03273313 0.18753142 0.02538325 0.0010288814 0.03415561 0.0006183714
## 81 81 0.03273702 0.18735078 0.02538304 0.0010282931 0.03407795 0.0006118771
## 82 82 0.03274299 0.18714531 0.02539701 0.0010228526 0.03416576 0.0006069899
## 83 83 0.03275191 0.18674431 0.02540849 0.0010168319 0.03429298 0.0006018370
## 84 84 0.03275533 0.18661884 0.02541683 0.0010305542 0.03445081 0.0006140984
## 85 85 0.03276109 0.18637832 0.02542296 0.0010319170 0.03436306 0.0006123312
## 86 86 0.03275271 0.18676943 0.02541477 0.0010365623 0.03448032 0.0006130590
## 87 87 0.03275085 0.18683660 0.02540482 0.0010329945 0.03391209 0.0006082194
## 88 88 0.03275558 0.18659036 0.02541449 0.0010249052 0.03350529 0.0005980305
## 89 89 0.03275130 0.18680618 0.02540771 0.0010225812 0.03349312 0.0005912777
## 90 90 0.03274594 0.18704682 0.02540109 0.0010197449 0.03359319 0.0005842610
## 91 91 0.03275006 0.18688455 0.02540132 0.0010248638 0.03339890 0.0005852373
## 92 92 0.03275331 0.18673982 0.02540381 0.0010204365 0.03325324 0.0005836473
## 93 93 0.03275648 0.18660385 0.02540999 0.0010238662 0.03333798 0.0005899686
## 94 94 0.03274958 0.18692970 0.02540860 0.0010116514 0.03317192 0.0005919200
## 95 95 0.03273868 0.18744788 0.02539715 0.0010163919 0.03315470 0.0005976378
## 96 96 0.03273149 0.18779947 0.02539344 0.0010166997 0.03328330 0.0006008236
## 97 97 0.03273029 0.18786826 0.02539032 0.0010244333 0.03357123 0.0006056640
## 98 98 0.03273080 0.18787056 0.02539207 0.0010104930 0.03358452 0.0005958696
## 99 99 0.03272810 0.18803368 0.02539175 0.0010137891 0.03378287 0.0005986268
## 100 100 0.03272301 0.18824349 0.02539125 0.0010206948 0.03381989 0.0005978662
## 101 101 0.03272920 0.18795645 0.02539981 0.0010240915 0.03386609 0.0005944838
## 102 102 0.03272849 0.18801247 0.02539960 0.0010276786 0.03380193 0.0005966001
## 103 103 0.03272510 0.18816484 0.02539236 0.0010257268 0.03375440 0.0005951537
## 104 104 0.03273079 0.18797972 0.02540040 0.0010325908 0.03401229 0.0006042888
## 105 105 0.03272391 0.18831989 0.02539238 0.0010324947 0.03421325 0.0006057019
## 106 106 0.03273503 0.18787238 0.02540413 0.0010377774 0.03442339 0.0006134727
## 107 107 0.03273528 0.18787285 0.02540490 0.0010400810 0.03430067 0.0006150265
## 108 108 0.03272783 0.18821344 0.02539738 0.0010422622 0.03432022 0.0006228197
## 109 109 0.03272983 0.18811025 0.02539221 0.0010406590 0.03413780 0.0006227490
## 110 110 0.03273085 0.18807574 0.02538730 0.0010418965 0.03392532 0.0006195427
## 111 111 0.03273212 0.18800040 0.02538795 0.0010329692 0.03364180 0.0006130944
## 112 112 0.03273683 0.18775618 0.02538907 0.0010264433 0.03347160 0.0006038173
## 113 113 0.03273756 0.18775911 0.02538796 0.0010275569 0.03374325 0.0006030993
## 114 114 0.03274041 0.18761830 0.02538593 0.0010270854 0.03368049 0.0006029527
## 115 115 0.03274551 0.18738119 0.02538824 0.0010294860 0.03345724 0.0006024729
## 116 116 0.03274389 0.18744889 0.02538653 0.0010323134 0.03328277 0.0006058579
## 117 117 0.03274602 0.18735540 0.02539042 0.0010277931 0.03332876 0.0005996376
## 118 118 0.03274361 0.18748651 0.02538897 0.0010279936 0.03369465 0.0006009555
## 119 119 0.03273670 0.18780619 0.02538066 0.0010291764 0.03396010 0.0006065886
## 120 120 0.03273896 0.18770059 0.02538110 0.0010312515 0.03376811 0.0006032755
## 121 121 0.03273789 0.18774169 0.02537867 0.0010366808 0.03375552 0.0006053470
## 122 122 0.03273628 0.18783880 0.02537426 0.0010359416 0.03395179 0.0006074492
## 123 123 0.03273583 0.18786227 0.02537592 0.0010390961 0.03391936 0.0006073419
## 124 124 0.03273042 0.18809748 0.02537206 0.0010363843 0.03393317 0.0006048800
## 125 125 0.03273460 0.18790452 0.02537577 0.0010340742 0.03375031 0.0006041654
## 126 126 0.03273081 0.18807814 0.02537257 0.0010313721 0.03379566 0.0006016746
## 127 127 0.03273348 0.18795871 0.02537387 0.0010304346 0.03391211 0.0006032236
## 128 128 0.03273482 0.18789408 0.02537281 0.0010306645 0.03393882 0.0006056804
## 129 129 0.03273502 0.18789667 0.02537506 0.0010317609 0.03392485 0.0006048815
## 130 130 0.03273317 0.18799893 0.02537240 0.0010349140 0.03409805 0.0006096305
## 131 131 0.03273157 0.18808191 0.02536922 0.0010360207 0.03425999 0.0006123594
## 132 132 0.03272728 0.18826976 0.02536604 0.0010376921 0.03440363 0.0006137921
## 133 133 0.03272652 0.18829927 0.02536554 0.0010345628 0.03436332 0.0006095151
## 134 134 0.03272717 0.18824400 0.02536648 0.0010316031 0.03413291 0.0006063551
## 135 135 0.03272861 0.18818103 0.02536766 0.0010319885 0.03406399 0.0006070329
## 136 136 0.03272840 0.18817615 0.02536682 0.0010306691 0.03391950 0.0006046425
## 137 137 0.03272914 0.18815963 0.02536852 0.0010303920 0.03395362 0.0006029156
## 138 138 0.03272688 0.18825322 0.02536591 0.0010303373 0.03390046 0.0006014799
## 139 139 0.03272841 0.18818724 0.02536586 0.0010287661 0.03384073 0.0005987557
## 140 140 0.03272766 0.18822236 0.02536378 0.0010283025 0.03386597 0.0005988105
## 141 141 0.03272988 0.18812177 0.02536553 0.0010277518 0.03388808 0.0005997787
## 142 142 0.03272945 0.18813972 0.02536681 0.0010285129 0.03389507 0.0005996815
## 143 143 0.03273172 0.18803401 0.02536858 0.0010271318 0.03379862 0.0005983827
## 144 144 0.03273118 0.18805575 0.02536741 0.0010272286 0.03379135 0.0005984701
## 145 145 0.03273142 0.18803956 0.02536675 0.0010269212 0.03380784 0.0005989952
## 146 146 0.03273038 0.18808519 0.02536570 0.0010274374 0.03380405 0.0006001165
## 147 147 0.03273117 0.18805072 0.02536742 0.0010282407 0.03378384 0.0006002984
## 148 148 0.03273148 0.18803306 0.02536851 0.0010276387 0.03379042 0.0006005813
## 149 149 0.03273186 0.18801995 0.02536907 0.0010268925 0.03377052 0.0006005685
## 150 150 0.03273175 0.18802377 0.02536901 0.0010264534 0.03376062 0.0005998615
## 151 151 0.03273158 0.18802911 0.02536848 0.0010261612 0.03374164 0.0006001690
## 152 152 0.03273137 0.18803677 0.02536861 0.0010261549 0.03374407 0.0005998615
## 153 153 0.03273170 0.18802270 0.02536903 0.0010260366 0.03374201 0.0006000006
## 154 154 0.03273175 0.18801994 0.02536914 0.0010263029 0.03375111 0.0006003751
## 155 155 0.03273174 0.18801812 0.02536919 0.0010261404 0.03374596 0.0006003774
## 156 156 0.03273170 0.18801970 0.02536912 0.0010260694 0.03374294 0.0006003263
## [1] "Best Model"
## nvmax
## 60 60
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 2.096734e+00 2.095889e+00 2.097578e+00
## PC1 2.864714e-04 2.298585e-04 3.430843e-04
## PC2 -3.807254e-04 -4.475032e-04 -3.139476e-04
## PC3 -8.108879e-05 -1.610158e-04 -1.161790e-06
## PC4 -8.943715e-05 -1.717642e-04 -7.110109e-06
## PC5 -2.377410e-04 -3.203356e-04 -1.551464e-04
## PC6 1.066122e-04 2.221774e-05 1.910067e-04
## PC7 -1.681047e-04 -2.536784e-04 -8.253090e-05
## PC8 -1.304845e-04 -2.183161e-04 -4.265283e-05
## PC9 1.005409e-04 9.396046e-06 1.916858e-04
## PC11 4.782470e-04 3.808854e-04 5.756087e-04
## PC12 -3.662753e-04 -4.641971e-04 -2.683536e-04
## PC13 3.070715e-04 2.060052e-04 4.081378e-04
## PC14 5.442716e-04 4.419095e-04 6.466337e-04
## PC15 -1.126470e-04 -2.179876e-04 -7.306318e-06
## PC16 2.139724e-04 1.042408e-04 3.237040e-04
## PC20 4.000364e-04 2.677662e-04 5.323067e-04
## PC21 -3.549027e-04 -4.930481e-04 -2.167573e-04
## PC22 1.860156e-03 1.714040e-03 2.006272e-03
## PC23 -5.033151e-04 -9.217876e-04 -8.484262e-05
## PC25 4.304268e-04 -3.069138e-05 8.915450e-04
## PC37 6.740412e-04 5.728323e-05 1.290799e-03
## PC39 -7.536803e-04 -1.373151e-03 -1.342099e-04
## PC47 -6.216417e-04 -1.265883e-03 2.260009e-05
## PC50 6.637683e-04 6.747998e-06 1.320789e-03
## PC52 -1.184340e-03 -1.851822e-03 -5.168588e-04
## PC57 5.712924e-04 -1.157284e-04 1.258313e-03
## PC58 1.048528e-03 3.606851e-04 1.736372e-03
## PC61 8.429992e-04 1.466646e-04 1.539334e-03
## PC63 6.993862e-04 -1.444877e-07 1.398917e-03
## PC67 -6.397041e-04 -1.352111e-03 7.270237e-05
## PC69 1.044065e-03 3.339378e-04 1.754192e-03
## PC72 9.661565e-04 2.474483e-04 1.684865e-03
## PC77 1.105688e-03 3.790291e-04 1.832347e-03
## PC79 -1.009839e-03 -1.736829e-03 -2.828478e-04
## PC85 -5.895932e-04 -1.324399e-03 1.452122e-04
## PC87 -1.047616e-03 -1.782099e-03 -3.131339e-04
## PC90 -6.935265e-04 -1.432596e-03 4.554267e-05
## PC93 6.296589e-04 -1.177987e-04 1.377116e-03
## PC98 6.428428e-04 -1.070484e-04 1.392734e-03
## PC99 -1.363831e-03 -2.115953e-03 -6.117087e-04
## PC107 -1.270600e-03 -2.028160e-03 -5.130396e-04
## PC111 -8.857512e-04 -1.648669e-03 -1.228339e-04
## PC112 -1.168778e-03 -1.932519e-03 -4.050357e-04
## PC115 -8.263315e-04 -1.594540e-03 -5.812314e-05
## PC116 1.385187e-03 6.246659e-04 2.145707e-03
## PC117 8.163043e-04 4.737984e-05 1.585229e-03
## PC118 9.866072e-04 2.207404e-04 1.752474e-03
## PC122 -1.390951e-03 -2.157106e-03 -6.247957e-04
## PC126 9.561386e-04 1.766049e-04 1.735672e-03
## PC127 -1.070588e-03 -1.850154e-03 -2.910221e-04
## PC133 -1.214145e-03 -1.995517e-03 -4.327725e-04
## PC134 6.879742e-04 -9.600879e-05 1.471957e-03
## PC137 -8.324059e-04 -1.625185e-03 -3.962735e-05
## PC139 -7.629960e-04 -1.558015e-03 3.202295e-05
## PC143 1.136332e-03 3.444744e-04 1.928190e-03
## PC144 6.994141e-04 -9.858229e-05 1.497410e-03
## PC146 2.334270e-03 1.535459e-03 3.133081e-03
## PC152 -1.296909e-03 -2.097718e-03 -4.961007e-04
## PC153 -6.618241e-04 -1.462808e-03 1.391600e-04
## PC154 7.113556e-04 -9.418126e-05 1.516892e-03Test
if (algo.forward.caret == TRUE){
test.model(model=model.forward, test=data.test
,method = 'leapForward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.034 2.085 2.097 2.097 2.110 2.148
## [1] "leapForward Test MSE: 0.00105127042865879"
Backward Elimination with CV
Train
if (algo.backward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapBackward"
,feature.names = feature.names)
model.backward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 60 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03460715 0.08910629 0.02686885 0.0011220847 0.02445943 0.0006474464
## 2 2 0.03427537 0.10669480 0.02663179 0.0010083889 0.02883392 0.0005758770
## 3 3 0.03411994 0.11496880 0.02653867 0.0010265906 0.03075293 0.0006063719
## 4 4 0.03379615 0.13189897 0.02630712 0.0010207545 0.03344351 0.0005144619
## 5 5 0.03350142 0.14741335 0.02600541 0.0011291975 0.04089043 0.0006240441
## 6 6 0.03335616 0.15492598 0.02585664 0.0011817548 0.04260564 0.0006431018
## 7 7 0.03334671 0.15524765 0.02588207 0.0011918151 0.04207618 0.0006350839
## 8 8 0.03331117 0.15702802 0.02587148 0.0011827844 0.04160488 0.0006327650
## 9 9 0.03322305 0.16163226 0.02580335 0.0012175344 0.04406315 0.0006238541
## 10 10 0.03304920 0.17039248 0.02567687 0.0012542700 0.04567367 0.0006956817
## 11 11 0.03294153 0.17540794 0.02559498 0.0012363522 0.04359549 0.0007022903
## 12 12 0.03302015 0.17164164 0.02563644 0.0012557230 0.04412034 0.0006919223
## 13 13 0.03305043 0.17016840 0.02564263 0.0012468449 0.04189529 0.0007132106
## 14 14 0.03301946 0.17187785 0.02562588 0.0012420740 0.04196257 0.0006972580
## 15 15 0.03304794 0.17044746 0.02565163 0.0012271977 0.04033782 0.0006823314
## 16 16 0.03304618 0.17060985 0.02566269 0.0012216908 0.04034003 0.0006564886
## 17 17 0.03302631 0.17169036 0.02566679 0.0012273896 0.04149103 0.0006758318
## 18 18 0.03299358 0.17333306 0.02564312 0.0012334455 0.04215032 0.0006963940
## 19 19 0.03296701 0.17451230 0.02564028 0.0012021627 0.04090036 0.0006805821
## 20 20 0.03295161 0.17520514 0.02562301 0.0011632949 0.03937627 0.0006490421
## 21 21 0.03294342 0.17569547 0.02561491 0.0011339592 0.03845149 0.0006403542
## 22 22 0.03296495 0.17490667 0.02562498 0.0011555594 0.03944700 0.0006626812
## 23 23 0.03294635 0.17573083 0.02558977 0.0011508121 0.03910113 0.0006454214
## 24 24 0.03293715 0.17617527 0.02558442 0.0011674877 0.03834398 0.0006736806
## 25 25 0.03291930 0.17704289 0.02556458 0.0011711946 0.03825170 0.0006768927
## 26 26 0.03287788 0.17907243 0.02551585 0.0011765267 0.03867622 0.0006855546
## 27 27 0.03288472 0.17889913 0.02553718 0.0011702651 0.03954319 0.0006737343
## 28 28 0.03285560 0.18010664 0.02550215 0.0011583478 0.03826274 0.0006693062
## 29 29 0.03284185 0.18091676 0.02547300 0.0011530386 0.03879046 0.0006477823
## 30 30 0.03280537 0.18266975 0.02546378 0.0011495330 0.03901952 0.0006397595
## 31 31 0.03279901 0.18309691 0.02544541 0.0011646416 0.03919244 0.0006336598
## 32 32 0.03280638 0.18267257 0.02544309 0.0011471350 0.03728355 0.0006035704
## 33 33 0.03279398 0.18328647 0.02543037 0.0011243804 0.03696881 0.0005880315
## 34 34 0.03277028 0.18445467 0.02540484 0.0011235998 0.03730505 0.0006068126
## 35 35 0.03274883 0.18530440 0.02539191 0.0011135069 0.03586909 0.0006076907
## 36 36 0.03274507 0.18551295 0.02539207 0.0010892369 0.03574803 0.0006177277
## 37 37 0.03273283 0.18596732 0.02538464 0.0010481181 0.03410175 0.0005812428
## 38 38 0.03271812 0.18664667 0.02536959 0.0010337151 0.03370093 0.0005685931
## 39 39 0.03273822 0.18574310 0.02539413 0.0010344984 0.03346221 0.0005584500
## 40 40 0.03274135 0.18566898 0.02539934 0.0010299346 0.03326166 0.0005560800
## 41 41 0.03274131 0.18566491 0.02539085 0.0010216059 0.03263768 0.0005427220
## 42 42 0.03274178 0.18566328 0.02539768 0.0010029839 0.03240042 0.0005330497
## 43 43 0.03272714 0.18627988 0.02537984 0.0009931485 0.03176621 0.0005296900
## 44 44 0.03274908 0.18541148 0.02539573 0.0009972581 0.03252447 0.0005276035
## 45 45 0.03275325 0.18539350 0.02541582 0.0010009944 0.03346403 0.0005461326
## 46 46 0.03275542 0.18529239 0.02541128 0.0009914222 0.03250482 0.0005351964
## 47 47 0.03276933 0.18460853 0.02543274 0.0009681256 0.03126429 0.0005136176
## 48 48 0.03274988 0.18562391 0.02541908 0.0009804754 0.03176915 0.0005148088
## 49 49 0.03275553 0.18549823 0.02542525 0.0010007573 0.03211922 0.0005294594
## 50 50 0.03276518 0.18508657 0.02543262 0.0009898485 0.03169052 0.0005268329
## 51 51 0.03277534 0.18456973 0.02544177 0.0009896558 0.03086487 0.0005231317
## 52 52 0.03278702 0.18411787 0.02545322 0.0009884840 0.03086504 0.0005233604
## 53 53 0.03277158 0.18482715 0.02543859 0.0009888290 0.03073065 0.0005190932
## 54 54 0.03275569 0.18567027 0.02542204 0.0010037024 0.03145190 0.0005342170
## 55 55 0.03274858 0.18610955 0.02542327 0.0010200009 0.03227789 0.0005288334
## 56 56 0.03273439 0.18676675 0.02540536 0.0010313737 0.03210915 0.0005412121
## 57 57 0.03270573 0.18813669 0.02539744 0.0010476874 0.03240237 0.0005572162
## 58 58 0.03270979 0.18808059 0.02539751 0.0010551510 0.03266562 0.0005609570
## 59 59 0.03271178 0.18802159 0.02539465 0.0010524592 0.03227840 0.0005608017
## 60 60 0.03269266 0.18893497 0.02538453 0.0010585926 0.03303490 0.0005627345
## 61 61 0.03270653 0.18832407 0.02539257 0.0010603466 0.03324198 0.0005581100
## 62 62 0.03272789 0.18736542 0.02540479 0.0010550276 0.03285952 0.0005624865
## 63 63 0.03272030 0.18765641 0.02540052 0.0010545069 0.03269457 0.0005683311
## 64 64 0.03270704 0.18832722 0.02538969 0.0010477951 0.03282912 0.0005747758
## 65 65 0.03270227 0.18861382 0.02538261 0.0010417427 0.03304326 0.0005818183
## 66 66 0.03269917 0.18874452 0.02537871 0.0010456097 0.03351914 0.0005984833
## 67 67 0.03270317 0.18855892 0.02538448 0.0010334160 0.03302725 0.0005881168
## 68 68 0.03270527 0.18850237 0.02538364 0.0010441783 0.03354538 0.0006071791
## 69 69 0.03272367 0.18768989 0.02540209 0.0010475336 0.03348799 0.0006005127
## 70 70 0.03272955 0.18745657 0.02539438 0.0010442300 0.03353255 0.0006052834
## 71 71 0.03273484 0.18726898 0.02539376 0.0010367535 0.03347874 0.0006027592
## 72 72 0.03273453 0.18725948 0.02538632 0.0010391762 0.03314719 0.0006078312
## 73 73 0.03272839 0.18756128 0.02538198 0.0010300782 0.03318120 0.0006021088
## 74 74 0.03272702 0.18766547 0.02537814 0.0010236755 0.03378648 0.0006054991
## 75 75 0.03272151 0.18796897 0.02536932 0.0010207351 0.03387082 0.0006093350
## 76 76 0.03273155 0.18750763 0.02537749 0.0010264015 0.03372761 0.0006173888
## 77 77 0.03273453 0.18733429 0.02538198 0.0010197202 0.03342693 0.0006103005
## 78 78 0.03274608 0.18688896 0.02539000 0.0010301481 0.03411692 0.0006209598
## 79 79 0.03274246 0.18706965 0.02538996 0.0010313375 0.03417372 0.0006254173
## 80 80 0.03273985 0.18724204 0.02538688 0.0010272337 0.03417139 0.0006205032
## 81 81 0.03274295 0.18710479 0.02538757 0.0010274180 0.03404998 0.0006134103
## 82 82 0.03274165 0.18720303 0.02539787 0.0010220478 0.03427418 0.0006063048
## 83 83 0.03275302 0.18671987 0.02541056 0.0010176765 0.03432553 0.0006038851
## 84 84 0.03275669 0.18658343 0.02541857 0.0010315616 0.03449735 0.0006157346
## 85 85 0.03276244 0.18634348 0.02542515 0.0010328783 0.03440773 0.0006142841
## 86 86 0.03275300 0.18675775 0.02541514 0.0010367721 0.03449552 0.0006133972
## 87 87 0.03275085 0.18683660 0.02540482 0.0010329945 0.03391209 0.0006082194
## 88 88 0.03275558 0.18659036 0.02541449 0.0010249052 0.03350529 0.0005980305
## 89 89 0.03274938 0.18687668 0.02540380 0.0010179384 0.03340387 0.0005847973
## 90 90 0.03274650 0.18702034 0.02540064 0.0010210869 0.03362662 0.0005835311
## 91 91 0.03275006 0.18688455 0.02540132 0.0010248638 0.03339890 0.0005852373
## 92 92 0.03275331 0.18673982 0.02540381 0.0010204365 0.03325324 0.0005836473
## 93 93 0.03275648 0.18660385 0.02540999 0.0010238662 0.03333798 0.0005899686
## 94 94 0.03274958 0.18692970 0.02540860 0.0010116514 0.03317192 0.0005919200
## 95 95 0.03273868 0.18744788 0.02539715 0.0010163919 0.03315470 0.0005976378
## 96 96 0.03273448 0.18765647 0.02539152 0.0010201272 0.03332907 0.0006020619
## 97 97 0.03273178 0.18779492 0.02538923 0.0010230580 0.03338110 0.0006027204
## 98 98 0.03273268 0.18778564 0.02538895 0.0010095769 0.03344484 0.0005937327
## 99 99 0.03272935 0.18799604 0.02539432 0.0010135720 0.03379191 0.0005988461
## 100 100 0.03272615 0.18810639 0.02539415 0.0010192672 0.03391352 0.0005980475
## 101 101 0.03273274 0.18780812 0.02540364 0.0010215282 0.03401060 0.0005950691
## 102 102 0.03272588 0.18812232 0.02539921 0.0010260384 0.03387407 0.0005980094
## 103 103 0.03272704 0.18807822 0.02539417 0.0010290160 0.03385211 0.0005960393
## 104 104 0.03273079 0.18797972 0.02540040 0.0010325908 0.03401229 0.0006042888
## 105 105 0.03272391 0.18831989 0.02539238 0.0010324947 0.03421325 0.0006057019
## 106 106 0.03273503 0.18787238 0.02540413 0.0010377774 0.03442339 0.0006134727
## 107 107 0.03273528 0.18787285 0.02540490 0.0010400810 0.03430067 0.0006150265
## 108 108 0.03272783 0.18821344 0.02539738 0.0010422622 0.03432022 0.0006228197
## 109 109 0.03272983 0.18811025 0.02539221 0.0010406590 0.03413780 0.0006227490
## 110 110 0.03273085 0.18807574 0.02538730 0.0010418965 0.03392532 0.0006195427
## 111 111 0.03273212 0.18800040 0.02538795 0.0010329692 0.03364180 0.0006130944
## 112 112 0.03273683 0.18775618 0.02538907 0.0010264433 0.03347160 0.0006038173
## 113 113 0.03273756 0.18775911 0.02538796 0.0010275569 0.03374325 0.0006030993
## 114 114 0.03274041 0.18761830 0.02538593 0.0010270854 0.03368049 0.0006029527
## 115 115 0.03274551 0.18738119 0.02538824 0.0010294860 0.03345724 0.0006024729
## 116 116 0.03274389 0.18744889 0.02538653 0.0010323134 0.03328277 0.0006058579
## 117 117 0.03274602 0.18735540 0.02539042 0.0010277931 0.03332876 0.0005996376
## 118 118 0.03274361 0.18748651 0.02538897 0.0010279936 0.03369465 0.0006009555
## 119 119 0.03273670 0.18780619 0.02538066 0.0010291764 0.03396010 0.0006065886
## 120 120 0.03273896 0.18770059 0.02538110 0.0010312515 0.03376811 0.0006032755
## 121 121 0.03273789 0.18774169 0.02537867 0.0010366808 0.03375552 0.0006053470
## 122 122 0.03273628 0.18783880 0.02537426 0.0010359416 0.03395179 0.0006074492
## 123 123 0.03273755 0.18779303 0.02537801 0.0010382534 0.03389075 0.0006082796
## 124 124 0.03273215 0.18802725 0.02537419 0.0010355374 0.03390472 0.0006058616
## 125 125 0.03273460 0.18790452 0.02537577 0.0010340742 0.03375031 0.0006041654
## 126 126 0.03273081 0.18807814 0.02537257 0.0010313721 0.03379566 0.0006016746
## 127 127 0.03273348 0.18795871 0.02537387 0.0010304346 0.03391211 0.0006032236
## 128 128 0.03273482 0.18789408 0.02537281 0.0010306645 0.03393882 0.0006056804
## 129 129 0.03273502 0.18789667 0.02537506 0.0010317609 0.03392485 0.0006048815
## 130 130 0.03273430 0.18795268 0.02537367 0.0010344937 0.03411680 0.0006099635
## 131 131 0.03273050 0.18812428 0.02536982 0.0010365357 0.03428766 0.0006125780
## 132 132 0.03272728 0.18826976 0.02536604 0.0010376921 0.03440363 0.0006137921
## 133 133 0.03272652 0.18829927 0.02536554 0.0010345628 0.03436332 0.0006095151
## 134 134 0.03272717 0.18824400 0.02536648 0.0010316031 0.03413291 0.0006063551
## 135 135 0.03272861 0.18818103 0.02536766 0.0010319885 0.03406399 0.0006070329
## 136 136 0.03272840 0.18817615 0.02536682 0.0010306691 0.03391950 0.0006046425
## 137 137 0.03272914 0.18815963 0.02536852 0.0010303920 0.03395362 0.0006029156
## 138 138 0.03272688 0.18825322 0.02536591 0.0010303373 0.03390046 0.0006014799
## 139 139 0.03272841 0.18818724 0.02536586 0.0010287661 0.03384073 0.0005987557
## 140 140 0.03272766 0.18822236 0.02536378 0.0010283025 0.03386597 0.0005988105
## 141 141 0.03272988 0.18812177 0.02536553 0.0010277518 0.03388808 0.0005997787
## 142 142 0.03272945 0.18813972 0.02536681 0.0010285129 0.03389507 0.0005996815
## 143 143 0.03273172 0.18803401 0.02536858 0.0010271318 0.03379862 0.0005983827
## 144 144 0.03273118 0.18805575 0.02536741 0.0010272286 0.03379135 0.0005984701
## 145 145 0.03273142 0.18803956 0.02536675 0.0010269212 0.03380784 0.0005989952
## 146 146 0.03273038 0.18808519 0.02536570 0.0010274374 0.03380405 0.0006001165
## 147 147 0.03273117 0.18805072 0.02536742 0.0010282407 0.03378384 0.0006002984
## 148 148 0.03273148 0.18803306 0.02536851 0.0010276387 0.03379042 0.0006005813
## 149 149 0.03273186 0.18801995 0.02536907 0.0010268925 0.03377052 0.0006005685
## 150 150 0.03273183 0.18801984 0.02536907 0.0010266433 0.03376543 0.0005999739
## 151 151 0.03273162 0.18802704 0.02536856 0.0010262367 0.03374419 0.0006003124
## 152 152 0.03273137 0.18803677 0.02536861 0.0010261549 0.03374407 0.0005998615
## 153 153 0.03273170 0.18802270 0.02536903 0.0010260366 0.03374201 0.0006000006
## 154 154 0.03273175 0.18801994 0.02536914 0.0010263029 0.03375111 0.0006003751
## 155 155 0.03273174 0.18801812 0.02536919 0.0010261404 0.03374596 0.0006003774
## 156 156 0.03273170 0.18801970 0.02536912 0.0010260694 0.03374294 0.0006003263
## [1] "Best Model"
## nvmax
## 60 60
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 2.096734e+00 2.095889e+00 2.097578e+00
## PC1 2.864714e-04 2.298585e-04 3.430843e-04
## PC2 -3.807254e-04 -4.475032e-04 -3.139476e-04
## PC3 -8.108879e-05 -1.610158e-04 -1.161790e-06
## PC4 -8.943715e-05 -1.717642e-04 -7.110109e-06
## PC5 -2.377410e-04 -3.203356e-04 -1.551464e-04
## PC6 1.066122e-04 2.221774e-05 1.910067e-04
## PC7 -1.681047e-04 -2.536784e-04 -8.253090e-05
## PC8 -1.304845e-04 -2.183161e-04 -4.265283e-05
## PC9 1.005409e-04 9.396046e-06 1.916858e-04
## PC11 4.782470e-04 3.808854e-04 5.756087e-04
## PC12 -3.662753e-04 -4.641971e-04 -2.683536e-04
## PC13 3.070715e-04 2.060052e-04 4.081378e-04
## PC14 5.442716e-04 4.419095e-04 6.466337e-04
## PC15 -1.126470e-04 -2.179876e-04 -7.306318e-06
## PC16 2.139724e-04 1.042408e-04 3.237040e-04
## PC20 4.000364e-04 2.677662e-04 5.323067e-04
## PC21 -3.549027e-04 -4.930481e-04 -2.167573e-04
## PC22 1.860156e-03 1.714040e-03 2.006272e-03
## PC23 -5.033151e-04 -9.217876e-04 -8.484262e-05
## PC25 4.304268e-04 -3.069138e-05 8.915450e-04
## PC37 6.740412e-04 5.728323e-05 1.290799e-03
## PC39 -7.536803e-04 -1.373151e-03 -1.342099e-04
## PC47 -6.216417e-04 -1.265883e-03 2.260009e-05
## PC50 6.637683e-04 6.747998e-06 1.320789e-03
## PC52 -1.184340e-03 -1.851822e-03 -5.168588e-04
## PC57 5.712924e-04 -1.157284e-04 1.258313e-03
## PC58 1.048528e-03 3.606851e-04 1.736372e-03
## PC61 8.429992e-04 1.466646e-04 1.539334e-03
## PC63 6.993862e-04 -1.444877e-07 1.398917e-03
## PC67 -6.397041e-04 -1.352111e-03 7.270237e-05
## PC69 1.044065e-03 3.339378e-04 1.754192e-03
## PC72 9.661565e-04 2.474483e-04 1.684865e-03
## PC77 1.105688e-03 3.790291e-04 1.832347e-03
## PC79 -1.009839e-03 -1.736829e-03 -2.828478e-04
## PC85 -5.895932e-04 -1.324399e-03 1.452122e-04
## PC87 -1.047616e-03 -1.782099e-03 -3.131339e-04
## PC90 -6.935265e-04 -1.432596e-03 4.554267e-05
## PC93 6.296589e-04 -1.177987e-04 1.377116e-03
## PC98 6.428428e-04 -1.070484e-04 1.392734e-03
## PC99 -1.363831e-03 -2.115953e-03 -6.117087e-04
## PC107 -1.270600e-03 -2.028160e-03 -5.130396e-04
## PC111 -8.857512e-04 -1.648669e-03 -1.228339e-04
## PC112 -1.168778e-03 -1.932519e-03 -4.050357e-04
## PC115 -8.263315e-04 -1.594540e-03 -5.812314e-05
## PC116 1.385187e-03 6.246659e-04 2.145707e-03
## PC117 8.163043e-04 4.737984e-05 1.585229e-03
## PC118 9.866072e-04 2.207404e-04 1.752474e-03
## PC122 -1.390951e-03 -2.157106e-03 -6.247957e-04
## PC126 9.561386e-04 1.766049e-04 1.735672e-03
## PC127 -1.070588e-03 -1.850154e-03 -2.910221e-04
## PC133 -1.214145e-03 -1.995517e-03 -4.327725e-04
## PC134 6.879742e-04 -9.600879e-05 1.471957e-03
## PC137 -8.324059e-04 -1.625185e-03 -3.962735e-05
## PC139 -7.629960e-04 -1.558015e-03 3.202295e-05
## PC143 1.136332e-03 3.444744e-04 1.928190e-03
## PC144 6.994141e-04 -9.858229e-05 1.497410e-03
## PC146 2.334270e-03 1.535459e-03 3.133081e-03
## PC152 -1.296909e-03 -2.097718e-03 -4.961007e-04
## PC153 -6.618241e-04 -1.462808e-03 1.391600e-04
## PC154 7.113556e-04 -9.418126e-05 1.516892e-03Test
if (algo.backward.caret == TRUE){
test.model(model.backward, data.test
,method = 'leapBackward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.034 2.085 2.097 2.097 2.110 2.148
## [1] "leapBackward Test MSE: 0.00105127042865879"
Stepwise Selection with CV
Train
if (algo.stepwise.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapSeq"
,feature.names = feature.names)
model.stepwise = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 21 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03596827 0.01527512 0.02784873 0.0008825615 0.006983967 0.0004973760
## 2 2 0.03575392 0.02743041 0.02768393 0.0008225004 0.012005307 0.0003996057
## 3 3 0.03559100 0.03645637 0.02760432 0.0007565589 0.015046580 0.0003491449
## 4 4 0.03521623 0.05820690 0.02725501 0.0008120500 0.026133041 0.0003377191
## 5 5 0.03504569 0.06691536 0.02714897 0.0008683118 0.026560799 0.0003921311
## 6 6 0.03502016 0.06788875 0.02713994 0.0008683515 0.024237027 0.0003823853
## 7 7 0.03494874 0.07154979 0.02709469 0.0008759187 0.023547787 0.0003737225
## 8 8 0.03485154 0.07691164 0.02701881 0.0008845557 0.025484354 0.0004071258
## 9 9 0.03474539 0.08175798 0.02694702 0.0008798285 0.022240966 0.0004188303
## 10 10 0.03473831 0.08205722 0.02691589 0.0008735658 0.021275990 0.0004221505
## 11 11 0.03467281 0.08545058 0.02687814 0.0008590112 0.021741633 0.0004367692
## 12 12 0.03480051 0.07838011 0.02698333 0.0007736157 0.022396497 0.0003830715
## 13 13 0.03479003 0.07967316 0.02698113 0.0010144558 0.025800714 0.0005416168
## 14 14 0.03470861 0.08427002 0.02685605 0.0008561926 0.022475789 0.0003582521
## 15 15 0.03472035 0.08370827 0.02688634 0.0008174997 0.022799803 0.0003234209
## 16 16 0.03473846 0.08240525 0.02693034 0.0008690334 0.023843643 0.0004312217
## 17 17 0.03472856 0.08272831 0.02693944 0.0008762592 0.022490018 0.0004255057
## 18 18 0.03470802 0.08365234 0.02687973 0.0008204037 0.023552122 0.0004172611
## 19 19 0.03471436 0.08330441 0.02689963 0.0007927295 0.019590131 0.0003959860
## 20 20 0.03464868 0.08701104 0.02683826 0.0008400387 0.023194229 0.0003896163
## 21 21 0.03463457 0.08762411 0.02685159 0.0008402589 0.022592445 0.0004321247
## [1] "Best Model"
## nvmax
## 21 21
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 2.096700e+00 2.095793e+00 2.097608e+00
## PC1 2.873471e-04 2.265370e-04 3.481572e-04
## PC2 -3.749128e-04 -4.466321e-04 -3.031935e-04
## PC3 -8.988881e-05 -1.757190e-04 -4.058607e-06
## PC4 -9.456845e-05 -1.829814e-04 -6.155477e-06
## PC5 -2.370038e-04 -3.257068e-04 -1.483009e-04
## PC6 9.804339e-05 7.424745e-06 1.886620e-04
## PC7 -1.746993e-04 -2.666232e-04 -8.277543e-05
## PC8 -1.275751e-04 -2.219056e-04 -3.324452e-05
## PC9 8.338440e-05 -1.453646e-05 1.813053e-04
## PC10 -2.575589e-05 -1.266890e-04 7.517724e-05
## PC11 4.798348e-04 3.752480e-04 5.844216e-04
## PC12 -3.711748e-04 -4.763764e-04 -2.659731e-04
## PC13 2.934464e-04 1.849049e-04 4.019878e-04
## PC14 5.422023e-04 4.323119e-04 6.520927e-04
## PC15 -1.240986e-04 -2.372591e-04 -1.093813e-05
## PC16 2.136898e-04 9.582792e-05 3.315516e-04
## PC17 -9.631725e-05 -2.188520e-04 2.621754e-05
## PC18 -8.540462e-05 -2.123825e-04 4.157327e-05
## PC19 -8.935724e-05 -2.220067e-04 4.329220e-05
## PC20 4.024553e-04 2.603635e-04 5.445472e-04
## PC21 -3.428740e-04 -4.912106e-04 -1.945375e-04Test
if (algo.stepwise.caret == TRUE){
test.model(model.stepwise, data.test
,method = 'leapSeq',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.066 2.089 2.097 2.097 2.105 2.137
## [1] "leapSeq Test MSE: 0.00114591004507159"
LASSO with CV
Train
if (algo.LASSO.caret == TRUE){
set.seed(1)
tune.grid= expand.grid(alpha = 1,lambda = 10^seq(from=-4,to=-2,length=100))
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "glmnet"
,subopt = 'LASSO'
,tune.grid = tune.grid
,feature.names = feature.names)
model.LASSO.caret = returned$model
}## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 1, lambda = 0.000278 on full training set
## glmnet
##
## 5584 samples
## 156 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.0001000000 0.03264617 0.19050061 0.02531753
## 0.0001047616 0.03264333 0.19058621 0.02531631
## 0.0001097499 0.03264049 0.19067098 0.02531518
## 0.0001149757 0.03263765 0.19075605 0.02531403
## 0.0001204504 0.03263479 0.19084240 0.02531286
## 0.0001261857 0.03263191 0.19092996 0.02531162
## 0.0001321941 0.03262895 0.19102159 0.02531030
## 0.0001384886 0.03262595 0.19111612 0.02530898
## 0.0001450829 0.03262298 0.19120996 0.02530776
## 0.0001519911 0.03261995 0.19130827 0.02530658
## 0.0001592283 0.03261689 0.19140985 0.02530542
## 0.0001668101 0.03261392 0.19150902 0.02530440
## 0.0001747528 0.03261100 0.19160861 0.02530339
## 0.0001830738 0.03260814 0.19170855 0.02530243
## 0.0001917910 0.03260543 0.19180414 0.02530163
## 0.0002009233 0.03260285 0.19189897 0.02530097
## 0.0002104904 0.03260041 0.19199124 0.02530034
## 0.0002205131 0.03259822 0.19207768 0.02529981
## 0.0002310130 0.03259632 0.19215599 0.02529963
## 0.0002420128 0.03259478 0.19222372 0.02529978
## 0.0002535364 0.03259377 0.19227299 0.02530053
## 0.0002656088 0.03259310 0.19231464 0.02530148
## 0.0002782559 0.03259290 0.19234147 0.02530265
## 0.0002915053 0.03259345 0.19233991 0.02530446
## 0.0003053856 0.03259459 0.19231852 0.02530710
## 0.0003199267 0.03259628 0.19228169 0.02531004
## 0.0003351603 0.03259877 0.19221696 0.02531358
## 0.0003511192 0.03260168 0.19214680 0.02531752
## 0.0003678380 0.03260504 0.19206792 0.02532173
## 0.0003853529 0.03260895 0.19197809 0.02532603
## 0.0004037017 0.03261348 0.19187160 0.02533083
## 0.0004229243 0.03261894 0.19173342 0.02533606
## 0.0004430621 0.03262546 0.19155742 0.02534127
## 0.0004641589 0.03263330 0.19132763 0.02534727
## 0.0004862602 0.03264231 0.19105439 0.02535415
## 0.0005094138 0.03265283 0.19071994 0.02536249
## 0.0005336699 0.03266533 0.19030022 0.02537229
## 0.0005590810 0.03267939 0.18982037 0.02538297
## 0.0005857021 0.03269533 0.18925866 0.02539512
## 0.0006135907 0.03271238 0.18866657 0.02540827
## 0.0006428073 0.03273083 0.18801622 0.02542194
## 0.0006734151 0.03275060 0.18731692 0.02543636
## 0.0007054802 0.03277277 0.18650719 0.02545315
## 0.0007390722 0.03279569 0.18569250 0.02546972
## 0.0007742637 0.03281986 0.18483097 0.02548716
## 0.0008111308 0.03284570 0.18390046 0.02550662
## 0.0008497534 0.03287301 0.18290555 0.02552745
## 0.0008902151 0.03290287 0.18179441 0.02555105
## 0.0009326033 0.03293470 0.18058275 0.02557667
## 0.0009770100 0.03296788 0.17932061 0.02560348
## 0.0010235310 0.03300172 0.17802519 0.02563139
## 0.0010722672 0.03303755 0.17662886 0.02566159
## 0.0011233240 0.03307408 0.17519814 0.02569179
## 0.0011768120 0.03311236 0.17368135 0.02572281
## 0.0012328467 0.03315216 0.17207884 0.02575507
## 0.0012915497 0.03319215 0.17049148 0.02578759
## 0.0013530478 0.03323174 0.16892805 0.02581893
## 0.0014174742 0.03327172 0.16739570 0.02585047
## 0.0014849683 0.03331209 0.16585601 0.02588300
## 0.0015556761 0.03335248 0.16437538 0.02591443
## 0.0016297508 0.03339369 0.16286823 0.02594559
## 0.0017073526 0.03343780 0.16121539 0.02597811
## 0.0017886495 0.03348485 0.15939740 0.02601254
## 0.0018738174 0.03353565 0.15736699 0.02604923
## 0.0019630407 0.03359084 0.15506051 0.02608890
## 0.0020565123 0.03365030 0.15247751 0.02613131
## 0.0021544347 0.03371297 0.14965928 0.02617645
## 0.0022570197 0.03377439 0.14699863 0.02622093
## 0.0023644894 0.03383637 0.14427806 0.02626614
## 0.0024770764 0.03389602 0.14178557 0.02631099
## 0.0025950242 0.03395421 0.13939413 0.02635518
## 0.0027185882 0.03401455 0.13689149 0.02640045
## 0.0028480359 0.03407805 0.13417391 0.02644955
## 0.0029836472 0.03414600 0.13112237 0.02650256
## 0.0031257158 0.03421867 0.12767571 0.02655865
## 0.0032745492 0.03429249 0.12416060 0.02661536
## 0.0034304693 0.03436962 0.12032634 0.02667377
## 0.0035938137 0.03445246 0.11595031 0.02673546
## 0.0037649358 0.03454249 0.11084384 0.02680221
## 0.0039442061 0.03462973 0.10589733 0.02686471
## 0.0041320124 0.03471833 0.10067431 0.02692702
## 0.0043287613 0.03479782 0.09625030 0.02698389
## 0.0045348785 0.03486557 0.09266316 0.02703174
## 0.0047508102 0.03491900 0.09058711 0.02706985
## 0.0049770236 0.03496120 0.08955919 0.02710002
## 0.0052140083 0.03500055 0.08910629 0.02712801
## 0.0054622772 0.03503852 0.08910629 0.02715467
## 0.0057223677 0.03508015 0.08910629 0.02718372
## 0.0059948425 0.03512576 0.08910629 0.02721502
## 0.0062802914 0.03517575 0.08910629 0.02724997
## 0.0065793322 0.03523051 0.08910629 0.02728868
## 0.0068926121 0.03529051 0.08910629 0.02733148
## 0.0072208090 0.03535624 0.08910629 0.02737821
## 0.0075646333 0.03542822 0.08910629 0.02742987
## 0.0079248290 0.03550704 0.08910629 0.02748614
## 0.0083021757 0.03559334 0.08910629 0.02754791
## 0.0086974900 0.03568779 0.08910629 0.02761688
## 0.0091116276 0.03579116 0.08910629 0.02769299
## 0.0095454846 0.03590425 0.08910629 0.02777702
## 0.0100000000 0.03602794 0.08910629 0.02786833
##
## Tuning parameter 'alpha' was held constant at a value of 1
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.0002782559.
## alpha lambda
## 23 1 0.0002782559
## alpha lambda RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.0001000000 0.03264617 0.19050061 0.02531753 0.0010391610 0.03483077 0.0005906667
## 2 1 0.0001047616 0.03264333 0.19058621 0.02531631 0.0010395479 0.03487220 0.0005899917
## 3 1 0.0001097499 0.03264049 0.19067098 0.02531518 0.0010399594 0.03491636 0.0005893319
## 4 1 0.0001149757 0.03263765 0.19075605 0.02531403 0.0010403800 0.03496237 0.0005886005
## 5 1 0.0001204504 0.03263479 0.19084240 0.02531286 0.0010407647 0.03500907 0.0005877888
## 6 1 0.0001261857 0.03263191 0.19092996 0.02531162 0.0010411697 0.03505669 0.0005870308
## 7 1 0.0001321941 0.03262895 0.19102159 0.02531030 0.0010415061 0.03510122 0.0005862387
## 8 1 0.0001384886 0.03262595 0.19111612 0.02530898 0.0010419170 0.03515079 0.0005855428
## 9 1 0.0001450829 0.03262298 0.19120996 0.02530776 0.0010424546 0.03520452 0.0005849023
## 10 1 0.0001519911 0.03261995 0.19130827 0.02530658 0.0010430320 0.03526267 0.0005842578
## 11 1 0.0001592283 0.03261689 0.19140985 0.02530542 0.0010436396 0.03532259 0.0005834866
## 12 1 0.0001668101 0.03261392 0.19150902 0.02530440 0.0010442398 0.03538114 0.0005826240
## 13 1 0.0001747528 0.03261100 0.19160861 0.02530339 0.0010448427 0.03543877 0.0005817181
## 14 1 0.0001830738 0.03260814 0.19170855 0.02530243 0.0010454926 0.03550444 0.0005806012
## 15 1 0.0001917910 0.03260543 0.19180414 0.02530163 0.0010461488 0.03557436 0.0005795718
## 16 1 0.0002009233 0.03260285 0.19189897 0.02530097 0.0010467939 0.03564716 0.0005785177
## 17 1 0.0002104904 0.03260041 0.19199124 0.02530034 0.0010475499 0.03572468 0.0005775232
## 18 1 0.0002205131 0.03259822 0.19207768 0.02529981 0.0010483553 0.03580390 0.0005763826
## 19 1 0.0002310130 0.03259632 0.19215599 0.02529963 0.0010492431 0.03588722 0.0005752031
## 20 1 0.0002420128 0.03259478 0.19222372 0.02529978 0.0010499656 0.03597489 0.0005734529
## 21 1 0.0002535364 0.03259377 0.19227299 0.02530053 0.0010510432 0.03607682 0.0005718132
## 22 1 0.0002656088 0.03259310 0.19231464 0.02530148 0.0010521113 0.03619361 0.0005700688
## 23 1 0.0002782559 0.03259290 0.19234147 0.02530265 0.0010530598 0.03631507 0.0005683893
## 24 1 0.0002915053 0.03259345 0.19233991 0.02530446 0.0010540278 0.03643232 0.0005666868
## 25 1 0.0003053856 0.03259459 0.19231852 0.02530710 0.0010547601 0.03654456 0.0005644804
## 26 1 0.0003199267 0.03259628 0.19228169 0.02531004 0.0010557592 0.03666872 0.0005625164
## 27 1 0.0003351603 0.03259877 0.19221696 0.02531358 0.0010572123 0.03680619 0.0005610059
## 28 1 0.0003511192 0.03260168 0.19214680 0.02531752 0.0010592133 0.03696316 0.0005601259
## 29 1 0.0003678380 0.03260504 0.19206792 0.02532173 0.0010608028 0.03711231 0.0005591131
## 30 1 0.0003853529 0.03260895 0.19197809 0.02532603 0.0010627777 0.03728188 0.0005584367
## 31 1 0.0004037017 0.03261348 0.19187160 0.02533083 0.0010644463 0.03743832 0.0005578645
## 32 1 0.0004229243 0.03261894 0.19173342 0.02533606 0.0010663633 0.03760743 0.0005570984
## 33 1 0.0004430621 0.03262546 0.19155742 0.02534127 0.0010682242 0.03777523 0.0005558241
## 34 1 0.0004641589 0.03263330 0.19132763 0.02534727 0.0010703049 0.03794906 0.0005545771
## 35 1 0.0004862602 0.03264231 0.19105439 0.02535415 0.0010722409 0.03810568 0.0005532214
## 36 1 0.0005094138 0.03265283 0.19071994 0.02536249 0.0010745165 0.03829049 0.0005525844
## 37 1 0.0005336699 0.03266533 0.19030022 0.02537229 0.0010769427 0.03848692 0.0005528051
## 38 1 0.0005590810 0.03267939 0.18982037 0.02538297 0.0010801213 0.03871799 0.0005539442
## 39 1 0.0005857021 0.03269533 0.18925866 0.02539512 0.0010828536 0.03894120 0.0005546813
## 40 1 0.0006135907 0.03271238 0.18866657 0.02540827 0.0010860756 0.03925308 0.0005557353
## 41 1 0.0006428073 0.03273083 0.18801622 0.02542194 0.0010882388 0.03953049 0.0005563015
## 42 1 0.0006734151 0.03275060 0.18731692 0.02543636 0.0010915404 0.03985858 0.0005584790
## 43 1 0.0007054802 0.03277277 0.18650719 0.02545315 0.0010953362 0.04020707 0.0005623500
## 44 1 0.0007390722 0.03279569 0.18569250 0.02546972 0.0010996221 0.04064877 0.0005683640
## 45 1 0.0007742637 0.03281986 0.18483097 0.02548716 0.0011043472 0.04106177 0.0005749255
## 46 1 0.0008111308 0.03284570 0.18390046 0.02550662 0.0011100872 0.04152137 0.0005820458
## 47 1 0.0008497534 0.03287301 0.18290555 0.02552745 0.0011159568 0.04191968 0.0005889936
## 48 1 0.0008902151 0.03290287 0.18179441 0.02555105 0.0011223390 0.04235460 0.0005955250
## 49 1 0.0009326033 0.03293470 0.18058275 0.02557667 0.0011270351 0.04269561 0.0006013460
## 50 1 0.0009770100 0.03296788 0.17932061 0.02560348 0.0011310184 0.04310947 0.0006071993
## 51 1 0.0010235310 0.03300172 0.17802519 0.02563139 0.0011318220 0.04336018 0.0006109515
## 52 1 0.0010722672 0.03303755 0.17662886 0.02566159 0.0011325507 0.04354883 0.0006142600
## 53 1 0.0011233240 0.03307408 0.17519814 0.02569179 0.0011315167 0.04355640 0.0006141945
## 54 1 0.0011768120 0.03311236 0.17368135 0.02572281 0.0011302316 0.04357305 0.0006135238
## 55 1 0.0012328467 0.03315216 0.17207884 0.02575507 0.0011264677 0.04343639 0.0006096628
## 56 1 0.0012915497 0.03319215 0.17049148 0.02578759 0.0011239462 0.04338016 0.0006064364
## 57 1 0.0013530478 0.03323174 0.16892805 0.02581893 0.0011182308 0.04306682 0.0006003362
## 58 1 0.0014174742 0.03327172 0.16739570 0.02585047 0.0011142836 0.04289795 0.0005965800
## 59 1 0.0014849683 0.03331209 0.16585601 0.02588300 0.0011091016 0.04253441 0.0005931215
## 60 1 0.0015556761 0.03335248 0.16437538 0.02591443 0.0011043064 0.04237517 0.0005899353
## 61 1 0.0016297508 0.03339369 0.16286823 0.02594559 0.0010971908 0.04203414 0.0005844191
## 62 1 0.0017073526 0.03343780 0.16121539 0.02597811 0.0010911044 0.04169251 0.0005793136
## 63 1 0.0017886495 0.03348485 0.15939740 0.02601254 0.0010844155 0.04122444 0.0005725948
## 64 1 0.0018738174 0.03353565 0.15736699 0.02604923 0.0010786179 0.04072598 0.0005663857
## 65 1 0.0019630407 0.03359084 0.15506051 0.02608890 0.0010731706 0.04014885 0.0005601347
## 66 1 0.0020565123 0.03365030 0.15247751 0.02613131 0.0010680984 0.03951570 0.0005546348
## 67 1 0.0021544347 0.03371297 0.14965928 0.02617645 0.0010613887 0.03861427 0.0005486449
## 68 1 0.0022570197 0.03377439 0.14699863 0.02622093 0.0010598743 0.03815163 0.0005468074
## 69 1 0.0023644894 0.03383637 0.14427806 0.02626614 0.0010577537 0.03737807 0.0005460818
## 70 1 0.0024770764 0.03389602 0.14178557 0.02631099 0.0010576567 0.03696160 0.0005493582
## 71 1 0.0025950242 0.03395421 0.13939413 0.02635518 0.0010543863 0.03615023 0.0005509180
## 72 1 0.0027185882 0.03401455 0.13689149 0.02640045 0.0010513409 0.03544244 0.0005523349
## 73 1 0.0028480359 0.03407805 0.13417391 0.02644955 0.0010480716 0.03455029 0.0005528786
## 74 1 0.0029836472 0.03414600 0.13112237 0.02650256 0.0010459556 0.03355527 0.0005545817
## 75 1 0.0031257158 0.03421867 0.12767571 0.02655865 0.0010451349 0.03236190 0.0005588777
## 76 1 0.0032745492 0.03429249 0.12416060 0.02661536 0.0010463143 0.03148805 0.0005638633
## 77 1 0.0034304693 0.03436962 0.12032634 0.02667377 0.0010475164 0.03036571 0.0005674295
## 78 1 0.0035938137 0.03445246 0.11595031 0.02673546 0.0010474071 0.02921814 0.0005706782
## 79 1 0.0037649358 0.03454249 0.11084384 0.02680221 0.0010470303 0.02788112 0.0005741424
## 80 1 0.0039442061 0.03462973 0.10589733 0.02686471 0.0010454088 0.02695443 0.0005778314
## 81 1 0.0041320124 0.03471833 0.10067431 0.02692702 0.0010454736 0.02581079 0.0005835776
## 82 1 0.0043287613 0.03479782 0.09625030 0.02698389 0.0010484332 0.02569577 0.0005897269
## 83 1 0.0045348785 0.03486557 0.09266316 0.02703174 0.0010476059 0.02443738 0.0005894391
## 84 1 0.0047508102 0.03491900 0.09058711 0.02706985 0.0010453591 0.02480725 0.0005862564
## 85 1 0.0049770236 0.03496120 0.08955919 0.02710002 0.0010357366 0.02437395 0.0005785413
## 86 1 0.0052140083 0.03500055 0.08910629 0.02712801 0.0010297358 0.02445943 0.0005733879
## 87 1 0.0054622772 0.03503852 0.08910629 0.02715467 0.0010256853 0.02445943 0.0005696828
## 88 1 0.0057223677 0.03508015 0.08910629 0.02718372 0.0010214948 0.02445943 0.0005657025
## 89 1 0.0059948425 0.03512576 0.08910629 0.02721502 0.0010171657 0.02445943 0.0005618714
## 90 1 0.0062802914 0.03517575 0.08910629 0.02724997 0.0010127006 0.02445943 0.0005580693
## 91 1 0.0065793322 0.03523051 0.08910629 0.02728868 0.0010081035 0.02445943 0.0005532795
## 92 1 0.0068926121 0.03529051 0.08910629 0.02733148 0.0010033804 0.02445943 0.0005486457
## 93 1 0.0072208090 0.03535624 0.08910629 0.02737821 0.0009985389 0.02445943 0.0005436583
## 94 1 0.0075646333 0.03542822 0.08910629 0.02742987 0.0009935895 0.02445943 0.0005383811
## 95 1 0.0079248290 0.03550704 0.08910629 0.02748614 0.0009885451 0.02445943 0.0005329255
## 96 1 0.0083021757 0.03559334 0.08910629 0.02754791 0.0009834218 0.02445943 0.0005277015
## 97 1 0.0086974900 0.03568779 0.08910629 0.02761688 0.0009782393 0.02445943 0.0005218109
## 98 1 0.0091116276 0.03579116 0.08910629 0.02769299 0.0009730217 0.02445943 0.0005159837
## 99 1 0.0095454846 0.03590425 0.08910629 0.02777702 0.0009677975 0.02445943 0.0005114156
## 100 1 0.0100000000 0.03602794 0.08910629 0.02786833 0.0009626004 0.02445943 0.0005075965
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients"
## model.coef
## (Intercept) 2.096711e+00
## PC1 2.666222e-04
## PC2 -3.579258e-04
## PC3 -5.704718e-05
## PC4 -6.220090e-05
## PC5 -2.089476e-04
## PC6 7.693112e-05
## PC7 -1.405524e-04
## PC8 -1.023950e-04
## PC9 6.943889e-05
## PC11 4.414004e-04
## PC12 -3.323702e-04
## PC13 2.706144e-04
## PC14 5.090926e-04
## PC15 -7.901322e-05
## PC16 1.740467e-04
## PC17 -4.365366e-05
## PC18 -4.859943e-05
## PC19 -5.171185e-05
## PC20 3.554498e-04
## PC21 -3.096025e-04
## PC22 1.809404e-03
## PC23 -3.812967e-04
## PC25 2.685874e-04
## PC27 -2.008531e-06
## PC28 -4.254256e-07
## PC29 8.401885e-05
## PC31 -1.725935e-05
## PC32 1.400186e-06
## PC34 1.710036e-04
## PC37 4.292158e-04
## PC38 1.477531e-04
## PC39 -5.405397e-04
## PC41 1.674620e-04
## PC42 4.440227e-05
## PC45 1.902803e-04
## PC46 6.426631e-05
## PC47 -3.929390e-04
## PC48 1.513346e-04
## PC49 6.238624e-05
## PC50 4.447532e-04
## PC51 -1.513102e-04
## PC52 -9.707285e-04
## PC53 -8.930141e-05
## PC55 1.279354e-04
## PC56 -1.460454e-04
## PC57 3.356608e-04
## PC58 8.314150e-04
## PC59 5.921425e-05
## PC61 5.985997e-04
## PC62 2.067079e-04
## PC63 4.395940e-04
## PC64 2.827211e-05
## PC67 -4.091865e-04
## PC69 8.392032e-04
## PC70 1.382275e-04
## PC72 7.217962e-04
## PC74 1.202940e-04
## PC75 1.962659e-04
## PC76 -9.753797e-05
## PC77 8.836147e-04
## PC78 -1.593700e-05
## PC79 -7.468496e-04
## PC80 -1.628806e-04
## PC81 1.326114e-04
## PC83 -1.391984e-04
## PC84 9.073742e-07
## PC85 -3.458962e-04
## PC86 -1.487096e-04
## PC87 -7.891685e-04
## PC88 8.998984e-07
## PC89 1.811490e-04
## PC90 -4.775714e-04
## PC91 2.741873e-04
## PC93 3.617266e-04
## PC95 2.265874e-04
## PC96 -7.764702e-05
## PC98 3.973032e-04
## PC99 -1.144240e-03
## PC100 -2.654442e-04
## PC101 2.812385e-05
## PC102 6.682435e-05
## PC103 -2.763091e-04
## PC105 -1.945439e-04
## PC107 -1.047838e-03
## PC108 6.802262e-05
## PC109 1.827916e-04
## PC111 -6.207813e-04
## PC112 -9.136307e-04
## PC113 2.936782e-04
## PC115 -5.709988e-04
## PC116 1.129284e-03
## PC117 5.580494e-04
## PC118 7.323012e-04
## PC119 -8.790013e-05
## PC120 3.241205e-04
## PC122 -1.143715e-03
## PC126 7.141219e-04
## PC127 -8.246701e-04
## PC130 3.316504e-04
## PC133 -9.641013e-04
## PC134 4.276815e-04
## PC137 -6.004540e-04
## PC139 -5.074014e-04
## PC140 9.236710e-05
## PC143 8.755517e-04
## PC144 4.392563e-04
## PC146 2.058305e-03
## PC148 -2.186550e-04
## PC150 -3.160812e-04
## PC152 -1.022602e-03
## PC153 -3.643977e-04
## PC154 4.195155e-04
## PC155 -2.588174e-04
## PC156 6.028137e-05Test
if (algo.LASSO.caret == TRUE){
test.model(model.LASSO.caret, data.test
,method = 'glmnet',subopt = "LASSO"
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.038 2.086 2.098 2.097 2.109 2.145
## [1] "glmnet LASSO Test MSE: 0.00104134602186552"
LARS with CV
Train
if (algo.LARS.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "lars"
,subopt = 'NULL'
,feature.names = feature.names)
model.LARS.caret = returned$model
}## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, : There were missing values in resampled
## performance measures.## Aggregating results
## Selecting tuning parameters
## Fitting fraction = 0.707 on full training set
## Least Angle Regression
##
## 5584 samples
## 156 predictor
##
## Pre-processing: centered (156), scaled (156)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ...
## Resampling results across tuning parameters:
##
## fraction RMSE Rsquared MAE
## 0.00000000 0.03622572 NaN 0.02801456
## 0.01010101 0.03587006 0.08910629 0.02775169
## 0.02020202 0.03555628 0.08910629 0.02752135
## 0.03030303 0.03528550 0.08910629 0.02732768
## 0.04040404 0.03505871 0.08910629 0.02716880
## 0.05050505 0.03488316 0.09168749 0.02704436
## 0.06060606 0.03473540 0.09964768 0.02693914
## 0.07070707 0.03459549 0.10785340 0.02684093
## 0.08080808 0.03445751 0.11587554 0.02673886
## 0.09090909 0.03432847 0.12257774 0.02664283
## 0.10101010 0.03421147 0.12814853 0.02655339
## 0.11111111 0.03410065 0.13328290 0.02646765
## 0.12121212 0.03399652 0.13771432 0.02638656
## 0.13131313 0.03390751 0.14128467 0.02631974
## 0.14141414 0.03382593 0.14467226 0.02625962
## 0.15151515 0.03374569 0.14822603 0.02620124
## 0.16161616 0.03366726 0.15176400 0.02614452
## 0.17171717 0.03359215 0.15503013 0.02609047
## 0.18181818 0.03352172 0.15794230 0.02604010
## 0.19191919 0.03345685 0.16050583 0.02599406
## 0.20202020 0.03340085 0.16259297 0.02595359
## 0.21212121 0.03335202 0.16434276 0.02591657
## 0.22222222 0.03330722 0.16600151 0.02588052
## 0.23232323 0.03326651 0.16755078 0.02584744
## 0.24242424 0.03322857 0.16904682 0.02581717
## 0.25252525 0.03319242 0.17047510 0.02578871
## 0.26262626 0.03315798 0.17182949 0.02576122
## 0.27272727 0.03312499 0.17313994 0.02573437
## 0.28282828 0.03309349 0.17439558 0.02570920
## 0.29292929 0.03306260 0.17563051 0.02568338
## 0.30303030 0.03303404 0.17674625 0.02565927
## 0.31313131 0.03300663 0.17781649 0.02563616
## 0.32323232 0.03298012 0.17884287 0.02561384
## 0.33333333 0.03295453 0.17982268 0.02559271
## 0.34343434 0.03292979 0.18077922 0.02557257
## 0.35353535 0.03290610 0.18168933 0.02555339
## 0.36363636 0.03288399 0.18252342 0.02553566
## 0.37373737 0.03286320 0.18330631 0.02551917
## 0.38383838 0.03284351 0.18403870 0.02550396
## 0.39393939 0.03282539 0.18469869 0.02549021
## 0.40404040 0.03280811 0.18532107 0.02547777
## 0.41414141 0.03279177 0.18590494 0.02546606
## 0.42424242 0.03277633 0.18644989 0.02545481
## 0.43434343 0.03276116 0.18700122 0.02544363
## 0.44444444 0.03274685 0.18751797 0.02543311
## 0.45454545 0.03273340 0.18799465 0.02542327
## 0.46464646 0.03272081 0.18843700 0.02541425
## 0.47474747 0.03270892 0.18884833 0.02540528
## 0.48484848 0.03269717 0.18926500 0.02539619
## 0.49494949 0.03268635 0.18964145 0.02538795
## 0.50505051 0.03267587 0.19001067 0.02537990
## 0.51515152 0.03266617 0.19034821 0.02537235
## 0.52525253 0.03265731 0.19064865 0.02536557
## 0.53535354 0.03264937 0.19090993 0.02535936
## 0.54545455 0.03264234 0.19112741 0.02535361
## 0.55555556 0.03263591 0.19131906 0.02534839
## 0.56565657 0.03262990 0.19149676 0.02534387
## 0.57575758 0.03262446 0.19165210 0.02533983
## 0.58585859 0.03261969 0.19177961 0.02533600
## 0.59595960 0.03261527 0.19189623 0.02533230
## 0.60606061 0.03261135 0.19199246 0.02532864
## 0.61616162 0.03260807 0.19206698 0.02532521
## 0.62626263 0.03260523 0.19212530 0.02532213
## 0.63636364 0.03260248 0.19218446 0.02531901
## 0.64646465 0.03260010 0.19223165 0.02531586
## 0.65656566 0.03259772 0.19228997 0.02531274
## 0.66666667 0.03259558 0.19234365 0.02530983
## 0.67676768 0.03259379 0.19238804 0.02530706
## 0.68686869 0.03259227 0.19242551 0.02530452
## 0.69696970 0.03259166 0.19242525 0.02530272
## 0.70707071 0.03259148 0.19241019 0.02530137
## 0.71717172 0.03259158 0.19238714 0.02530033
## 0.72727273 0.03259201 0.19235382 0.02529942
## 0.73737374 0.03259286 0.19230664 0.02529861
## 0.74747475 0.03259424 0.19224121 0.02529820
## 0.75757576 0.03259612 0.19216075 0.02529830
## 0.76767677 0.03259847 0.19206367 0.02529877
## 0.77777778 0.03260109 0.19196236 0.02529948
## 0.78787879 0.03260410 0.19185176 0.02530030
## 0.79797980 0.03260743 0.19173238 0.02530128
## 0.80808081 0.03261107 0.19160626 0.02530271
## 0.81818182 0.03261504 0.19147127 0.02530418
## 0.82828283 0.03261935 0.19132618 0.02530598
## 0.83838384 0.03262362 0.19118942 0.02530765
## 0.84848485 0.03262818 0.19104692 0.02530967
## 0.85858586 0.03263299 0.19089918 0.02531181
## 0.86868687 0.03263792 0.19074977 0.02531388
## 0.87878788 0.03264317 0.19059301 0.02531601
## 0.88888889 0.03264890 0.19042055 0.02531859
## 0.89898990 0.03265493 0.19024135 0.02532135
## 0.90909091 0.03266130 0.19005233 0.02532465
## 0.91919192 0.03266801 0.18985243 0.02532818
## 0.92929293 0.03267515 0.18963945 0.02533212
## 0.93939394 0.03268250 0.18942299 0.02533642
## 0.94949495 0.03268999 0.18920674 0.02534106
## 0.95959596 0.03269774 0.18898459 0.02534619
## 0.96969697 0.03270579 0.18875475 0.02535147
## 0.97979798 0.03271415 0.18851592 0.02535696
## 0.98989899 0.03272282 0.18826960 0.02536285
## 1.00000000 0.03273170 0.18801970 0.02536912
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was fraction = 0.7070707.
## fraction
## 71 0.7070707## Warning: Removed 1 rows containing missing values (geom_point).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients"
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
## 3.979204e-03 -4.529032e-03 -6.041100e-04 -6.397054e-04 -2.138280e-03 7.716498e-04 -1.388493e-03 -9.861185e-04
## PC9 PC11 PC12 PC13 PC14 PC15 PC16 PC17
## 6.446563e-04 3.831253e-03 -2.867385e-03 2.263494e-03 4.203485e-03 -6.344864e-04 1.341472e-03 -3.243570e-04
## PC18 PC19 PC20 PC21 PC22 PC23 PC25 PC29
## -3.483269e-04 -3.548302e-04 2.270444e-03 -1.895473e-03 1.045870e-02 -7.708148e-04 4.930938e-04 1.395846e-04
## PC31 PC34 PC37 PC38 PC39 PC41 PC42 PC45
## -2.702427e-05 2.440591e-04 5.895480e-04 2.041306e-04 -7.384314e-04 2.258879e-04 6.065922e-05 2.527388e-04
## PC46 PC47 PC48 PC49 PC50 PC51 PC52 PC53
## 8.482054e-05 -5.163517e-04 1.964055e-04 8.212524e-05 5.727637e-04 -1.928417e-04 -1.230096e-03 -1.124879e-04
## PC55 PC56 PC57 PC58 PC59 PC61 PC62 PC63
## 1.616172e-04 -1.806301e-04 4.140550e-04 1.022022e-03 7.369336e-05 7.274535e-04 2.516309e-04 5.319542e-04
## PC64 PC67 PC69 PC70 PC72 PC74 PC75 PC76
## 3.540804e-05 -4.864265e-04 9.993174e-04 1.628052e-04 8.495550e-04 1.416114e-04 2.311658e-04 -1.148550e-04
## PC77 PC78 PC79 PC80 PC81 PC83 PC85 PC86
## 1.028472e-03 -1.983963e-05 -8.689957e-04 -1.900813e-04 1.547005e-04 -1.613707e-04 -3.989476e-04 -1.709126e-04
## PC87 PC89 PC90 PC91 PC93 PC95 PC96 PC98
## -9.085835e-04 2.083146e-04 -5.471581e-04 3.104819e-04 4.099485e-04 2.586501e-04 -8.919372e-05 4.487015e-04
## PC99 PC100 PC101 PC102 PC103 PC105 PC107 PC108
## -1.286102e-03 -2.982126e-04 3.264192e-05 7.582708e-05 -3.102867e-04 -2.161974e-04 -1.169304e-03 7.688916e-05
## PC109 PC111 PC112 PC113 PC115 PC116 PC117 PC118
## 2.018792e-04 -6.883543e-04 -1.011828e-03 3.266372e-04 -6.289574e-04 1.255450e-03 6.142997e-04 8.087562e-04
## PC119 PC120 PC122 PC126 PC127 PC130 PC133 PC134
## -9.771394e-05 3.556935e-04 -1.261866e-03 7.747775e-04 -8.947624e-04 3.592737e-04 -1.043070e-03 4.618132e-04
## PC137 PC139 PC140 PC143 PC144 PC146 PC148 PC150
## -6.409746e-04 -5.402092e-04 9.978505e-05 9.349360e-04 4.660234e-04 2.177732e-03 -2.316716e-04 -3.348448e-04
## PC152 PC153 PC154 PC155 PC156
## -1.079600e-03 -3.857370e-04 4.412399e-04 -2.723591e-04 6.441860e-05Test
if (algo.LARS.caret == TRUE){
test.model(model.LARS.caret, data.test
,method = 'lars',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.038 2.086 2.098 2.097 2.109 2.145
## [1] "lars Test MSE: 0.00104132775293204"
Session Info
sessionInfo()## R version 3.5.1 (2018-07-02)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 17134)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252 LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C LC_TIME=English_United States.1252
##
## attached base packages:
## [1] parallel stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] bindrcpp_0.2.2 knitr_1.20 htmltools_0.3.6 reshape2_1.4.3
## [5] lars_1.2 doParallel_1.0.14 iterators_1.0.10 caret_6.0-81
## [9] leaps_3.0 ggforce_0.1.3 rlist_0.4.6.1 car_3.0-2
## [13] carData_3.0-2 bestNormalize_1.3.0 scales_1.0.0 onewaytests_2.0
## [17] caTools_1.17.1.1 mosaic_1.5.0 mosaicData_0.17.0 ggformula_0.9.1
## [21] ggstance_0.3.1 lattice_0.20-35 DT_0.5 ggiraph_0.6.0
## [25] investr_1.4.0 glmnet_2.0-16 foreach_1.4.4 Matrix_1.2-14
## [29] MASS_7.3-50 PerformanceAnalytics_1.5.2 xts_0.11-2 zoo_1.8-4
## [33] forcats_0.3.0 stringr_1.3.1 dplyr_0.7.8 purrr_0.2.5
## [37] readr_1.3.1 tidyr_0.8.2 tibble_1.4.2 ggplot2_3.1.0
## [41] tidyverse_1.2.1 usdm_1.1-18 raster_2.8-4 sp_1.3-1
## [45] pacman_0.5.0
##
## loaded via a namespace (and not attached):
## [1] readxl_1.2.0 backports_1.1.3 plyr_1.8.4 lazyeval_0.2.1 splines_3.5.1 mycor_0.1.1
## [7] crosstalk_1.0.0 leaflet_2.0.2 digest_0.6.18 magrittr_1.5 mosaicCore_0.6.0 openxlsx_4.1.0
## [13] recipes_0.1.4 modelr_0.1.2 gower_0.1.2 colorspace_1.3-2 rvest_0.3.2 ggrepel_0.8.0
## [19] haven_2.0.0 crayon_1.3.4 jsonlite_1.5 bindr_0.1.1 survival_2.42-3 glue_1.3.0
## [25] registry_0.5 gtable_0.2.0 ppcor_1.1 ipred_0.9-8 abind_1.4-5 rngtools_1.3.1
## [31] bibtex_0.4.2 Rcpp_1.0.0 xtable_1.8-3 units_0.6-2 foreign_0.8-70 stats4_3.5.1
## [37] lava_1.6.4 prodlim_2018.04.18 htmlwidgets_1.3 httr_1.4.0 RColorBrewer_1.1-2 pkgconfig_2.0.2
## [43] farver_1.1.0 nnet_7.3-12 labeling_0.3 tidyselect_0.2.5 rlang_0.3.1 later_0.7.5
## [49] munsell_0.5.0 cellranger_1.1.0 tools_3.5.1 cli_1.0.1 generics_0.0.2 moments_0.14
## [55] sjlabelled_1.0.17 broom_0.5.1 evaluate_0.12 ggdendro_0.1-20 yaml_2.2.0 ModelMetrics_1.2.2
## [61] zip_2.0.1 nlme_3.1-137 doRNG_1.7.1 mime_0.6 xml2_1.2.0 compiler_3.5.1
## [67] rstudioapi_0.8 curl_3.2 tweenr_1.0.1 stringi_1.2.4 gdtools_0.1.7 pillar_1.3.1
## [73] data.table_1.11.8 bitops_1.0-6 insight_0.1.2 httpuv_1.4.5 R6_2.3.0 promises_1.0.1
## [79] gridExtra_2.3 rio_0.5.16 codetools_0.2-15 assertthat_0.2.0 pkgmaker_0.27 withr_2.1.2
## [85] nortest_1.0-4 mgcv_1.8-24 hms_0.4.2 quadprog_1.5-5 grid_3.5.1 rpart_4.1-13
## [91] timeDate_3043.102 class_7.3-14 rmarkdown_1.11 shiny_1.2.0 lubridate_1.7.4